"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 ", 4624, " equivalence classes of generalized patterns of lengths ", [4, 4] "Class ", 1, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 564, 3652, 26986, 224458, 2073946, 21080922, 233752052, 2807949492, 36324988206, 503484183878, 7443797211854, 116931715588046, 1944883690208684, 34145703631815228, 631037086895761354] "" "Class ", 2, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]} "Class ", 3, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 3}, {[1, 0, 0, 0, 0]}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 378, 1590, 6520, 25576, 94480, 326288, 1056392, 3232152, 9429216, 26440192, 71740184, 189371080, 488419376, 1235094256, 3070733096] "" "Class ", 4, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]} "Class ", 5, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 544, 3458, 25134, 205500, 1866868, 18655340, 203367564, 2401723948, 30545632108, 416234774626, 6050013138206, 93433627521452, 1527825270511732, 26370918922301972, 479129854633911572] "" "Class ", 6, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]} "Class ", 7, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 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}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {1, 3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 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, 6, 22, 90, 392, 1768, 8106, 37334, 171532, 783300, 3549230, 15949618, 71094672, 314478752, 1381238194, 6027545742, 26150049812, 112852934524, 484716831798] "" "Class ", 8, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 9, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3430, 24806, 201888, 1825682, 18161242, 197083654, 2316958020, 29333883126, 397909455134, 5757415962966, 88511546508984, 1440773887089914, 24755564251557842, 447740339384196566] "" "Class ", 10, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 11, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 12, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "For the class ", {{[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 340, 1340, 5254, 20518, 79932, 311028, 1209916, 4707964, 18330728, 71429176, 278586182, 1087537414, 4249391468, 16618640836, 65048019092] "" "Class ", 13, " is:" {{[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 1, 4], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 544, 3458, 25134, 205524, 1867228, 18660048, 203430924, 2402617568, 30558887532, 416441144054, 6053385911614, 93491474252412, 1528865361437044, 26390497338535360, 479515117992414972] "" "Class ", 14, " is:" {{[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 15, " is:" {{[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 16, " is:" {{[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 17, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 556, 3543, 25818, 211638, 1926232, 19286906, 210669262, 2492717098, 31764050320, 433672018436, 6315576340946, 97722439526561, 1601028663061408, 27687565163278083, 504019001333513022] "" "Class ", 18, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 1, 0]]} "Class ", 19, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 477, 2629, 15836, 102920, 715140, 5275456, 41075030, 335978994, 2875805559, 25672661733, 238345817678, 2295574481632, 22886373741307, 235737578181387, 2504389167427798] "" "Class ", 20, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 1, 1]]} "Class ", 21, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 553, 3517, 25572, 209051, 1898690, 18969740, 206748447, 2441108159, 31039642442, 422872021574, 6145117203590, 94881224242919, 1551150564709879, 26767557364291849, 486227947497442728] "" "Class ", 22, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {2, 3, 4}, {}], [[4, 1, 3, 5, 2], {2, 3, 4}, {}], [[4, 2, 3, 5, 1], {2, 3, 4}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3057, 20492, 152388, 1243404, 11045844, 106059534, 1094215038, 12069431616, 141701636592, 1764041158272, 23206934462496, 321656231501640, 4684494358638792, 71511410924861616] "" "Class ", 23, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 24, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 25, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 560, 3607, 26558, 220132, 2026851, 20528168, 226823487, 2715069083, 34999143668, 483391157975, 7121447877434, 111472239467000, 1847518713447151, 32321539641575518, 595211918066849834] "" "Class ", 26, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 27, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 28, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 29, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 554, 3543, 25908, 213097, 1947511, 19578591, 214718312, 2551054037, 32640352349, 447458892585, 6543049792962, 101656753532409, 1672306316495635, 29038656597829676, 530778845933866244] "" "Class ", 30, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 31, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 32, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 33, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 565, 3677, 27304, 228256, 2120369, 21664079, 241471236, 2915803360, 37916931581, 528288539927, 7851241516564, 123975065212524, 2072783247924021, 36580914294737745, 679565960208873336] "" "Class ", 34, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 519, 3175, 21989, 169889, 1447462, 13473790, 135984373, 1478499905, 17223460478, 213968186454, 2823155757597, 39420306105441, 580664736420059, 8997480996904463, 146285741734041363] "" "Class ", 35, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 36, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 37, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 554, 3555, 26060, 214909, 1969259, 19849063, 218254572, 2599866831, 33352095163, 458414001233, 6720811564250, 104692227528309, 1726754819684965, 30062705433997710, 550936863737860737] "" "Class ", 38, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]} "Class ", 39, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {2, 3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 477, 2653, 16308, 109168, 788299, 6094395, 50124078, 436290292, 4001472721, 38526193025, 388136024247, 4080217509313, 44645858614175, 507372006113833, 5976823636403560] "" "Class ", 40, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 41, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]} "Class ", 42, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[1, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 471, 2553, 15081, 96033, 653108, 4713684, 35898076, 287168860, 2403922536, 20988360560, 190592123623, 1795696656091, 17515517915907, 176543147460297, 1835578224748298] "" "Class ", 43, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]} "Class ", 44, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [1, 0, 0]]}, {[[4, 3, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [1, 0, 0]]}, {[[4, 3, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 559, 3393, 23178, 176001, 1472509, 13465993, 133735533, 1434095090, 16522479492, 203615399618, 2673476656589, 37267969800935, 549802109860255, 8559246950588867, 140244303252112306] "" "Class ", 45, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2670, 16674, 114894, 865506, 7076764, 62408992, 590444210, 5964879162, 64083008326, 729521297454, 8771954617712, 111089767820204, 1477921798487134, 20607041771320778] "" "Class ", 46, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2662, 16536, 113146, 845558, 6857450, 59985862, 563071166, 5645592950, 60219029744, 680888489104, 8134748346088, 102397323259614, 1354510216832566, 18784677355045258] "" "Class ", 47, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 3, 4], [1, 0, 1]]}, {[[4, 3, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 3, 4], [1, 0, 1]]} "Class ", 48, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]} "Class ", 49, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [0, 1, 0]]} "Class ", 50, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]} "Class ", 51, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 1, 1]]} "Class ", 52, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "Class ", 53, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "Class ", 54, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 55, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 56, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 57, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 58, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 59, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 60, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 61, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 62, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 63, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 64, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "Class ", 65, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 66, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 67, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 68, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]} "Class ", 69, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]} "Class ", 70, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]} "Class ", 71, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 72, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[1, 0, 0, 0, 0]}], [[3, 1, 2, 4], {1}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[1, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {4}, {}], [[1, 3, 5, 4, 2], {4}, %1], [[1, 4, 5, 2, 3], {1, 2}, {}], [[1, 4, 5, 3, 2], {4}, %1], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {4}, {}], [[2, 3, 5, 4, 1], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {}], [[2, 4, 5, 3, 1], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {}], [[3, 4, 5, 2, 1], {4}, {[1, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 4}, %1], [[4, 2, 3, 1, 5], {1, 4}, {[1, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {4}, %1], [[5, 1, 3, 4, 2], {4}, %1], [[5, 1, 4, 2, 3], {2, 3}, %1], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {4}, {[1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} %1 := {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 414, 1968, 9739, 49923, 264225, 1440635, 8076775, 46485089, 274272683, 1656868145, 10236247688, 64608618196, 416225060055, 2734508719555, 18306203878719] "" "Class ", 73, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]} "Class ", 74, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 3, 4], [1, 1, 0]]} "Class ", 75, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}] , [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 1, 3, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {[1, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 1, 4], {3}, {[1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {3}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {[0, 0, 2, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3}, %3], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [1, 4, 3, 5, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, %3], [[2, 1, 4, 5, 3], {1, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3}, %3], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {4}, %2], [[2, 4, 3, 5, 1], {4}, %2], [[2, 5, 3, 1, 4], {1, 4}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {4}, %2], [[3, 2, 4, 5, 1], {4}, %2], [[3, 2, 5, 1, 4], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {4}, %2], [[3, 4, 2, 5, 1], {4}, %2], [[3, 5, 2, 1, 4], {1, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 2, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 2, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 1, 5], {4}, %2], [[4, 2, 3, 5, 1], {4}, %2], [[4, 2, 5, 1, 3], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3}, %1], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 4}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, %1], [[4, 5, 3, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 2, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 2, 3, 1, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {1, 2, 3}, %1], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} %1 := {[0, 0, 2, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]} %3 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 380, 1616, 6848, 29020, 123504, 528160, 2270470, 9811526, 42611312, 185937756, 814952568, 3586653324, 15845793042, 70256915822, 312540626822] "" "Class ", 76, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]} "Class ", 77, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 490, 2767, 17183, 115861, 840279, 6506517, 53471770, 464113812, 4237079563, 40544747976, 405434713799, 4225570240211, 45795587029899, 515043658114252, 5999964391295934] "" "Class ", 78, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]} "Class ", 79, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2336, 13104, 78288, 493896, 3270472, 22615464, 162670152, 1212975904, 9350571488, 74340383776, 608312875552, 5114065847104, 44102540457408, 389595453153216] "" "Class ", 80, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 1]]} "Class ", 81, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2550, 15208, 97931, 674647, 4936457, 38146884, 309854237, 2635178172, 23387137686, 215984959969, 2070516239652, 20559082440762, 211041967858062, 2235807353200365] "" "Class ", 82, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {1, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 433, 2225, 12311, 72525, 451090, 2943020, 20036957, 141760227, 1038613749, 7857195875, 61224071863, 490339539041, 4028961876057, 33908811620467, 291903781030201] "" "Class ", 83, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 84, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 85, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2604, 15856, 104813, 745724, 5668098, 45752112, 390317053, 3504896990, 33011543070, 325146044318, 3340133143361, 35703193084176, 396282668056981, 4558770404444321] "" "Class ", 86, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 87, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 88, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 89, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2650, 16275, 108357, 774746, 5906106, 47724197, 406798571, 3643141743, 34162762411, 334457269047, 3409832831814, 36120763775551, 396779038783453, 4511663607143504] "" "Class ", 90, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 91, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 92, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 93, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 477, 2704, 16893, 114976, 843812, 6623993, 55268073, 487588744, 4528693468, 44119660693, 449425148615, 4773691689410, 52744231644631, 604910723902691, 7187464215005247] "" "Class ", 94, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 95, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 96, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 97, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {}], [[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], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2530, 15148, 98753, 694023, 5218793, 41741903, 353332613, 3151674821, 29516472375, 289322995115, 2960030858164, 31531575346448, 348971959287338, 4004873517216612] "" "Class ", 98, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]} "Class ", 99, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[1, 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, 6, 22, 90, 398, 1874, 9310, 48538, 264670, 1505634, 8915838, 54846442, 349839390, 2309856210, 15762412510, 111010171514, 805814732510, 6021633834434, 46271607500094] "" "Class ", 100, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 101, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]} "Class ", 102, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 460, 2419, 13544, 79637, 487025, 3076230, 19963604, 132573461, 898025814, 6189063512, 43307035076, 307142045510, 2204648342116, 15996582725282, 117205827359726] "" "Class ", 103, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 0]]} "Class ", 104, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 105, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1837, 8864, 44074, 224352, 1163724, 6129840, 32703074, 176351644, 959658200, 5262988330, 29057961666, 161374413196, 900792925199, 5050924332096] "" "Class ", 106, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "Class ", 107, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "Class ", 108, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 109, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 0, 2]}], [[2, 1, 3], {1, 3}, {[0, 0, 0, 2], [0, 0, 1, 0]}], [[2, 3, 1], {2}, {[0, 0, 0, 2]}], [[3, 1, 2], {1}, {[0, 0, 0, 2]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 87382, 349526, 1398102, 5592406, 22369622, 89478486, 357913942, 1431655766, 5726623062, 22906492246, 91625968982] "" "Class ", 110, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 111, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 112, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 113, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 114, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 115, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 116, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "Class ", 117, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 118, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 119, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 120, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]} "Class ", 121, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]} "Class ", 122, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [ [4, 1, 2, 3], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [ [2, 5, 3, 1, 4], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 1, 2], {1, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 368, 1574, 6791, 29293, 125627, 533889, 2244229, 9322845, 38263095, 155172643, 622024396, 2465852748, 9672362056, 37562268680, 144501382440] "" "Class ", 123, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 124, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 554, 3530, 25703, 210477, 1914822, 19161539, 209178846, 2473808560, 31506343515, 429925584142, 6257736245203, 96776546749846, 1584698268555582, 27390763628158372, 498354164151098437] "" "Class ", 125, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 540, 3400, 24440, 197640, 1775728, 17550016, 189219888, 2210144080, 27800942912, 374681414880, 5386338532096, 82272397880704, 1330571673462528, 22714516689112576, 408173801110010624] "" "Class ", 126, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 552, 3556, 26158, 216504, 1991280, 20145752, 222341382, 2658403644, 34229970572, 472231747080, 6949164014358, 108652295739360, 1798741830857400, 31432567431667320, 578185601857131630] "" "Class ", 127, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 128, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 129, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2540, 15626, 105994, 785958, 6325138, 54907176, 511425284, 5087826926, 53842565626, 603962663246, 7158165556678, 89384005652578, 1172911600292766, 16136298607932164] "" "Class ", 130, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 131, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 132, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {4}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 2, 5], {4}, {}], [[1, 4, 3, 5, 2], {4}, {}], [[1, 5, 3, 2, 4], {1, 4}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {}], [[2, 1, 3, 4, 5], {4}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 4}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 1, 5], {4}, {}], [[2, 4, 3, 5, 1], {4}, {}], [[2, 5, 3, 1, 4], {1, 4}, {}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {4}, {}], [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 4}, {}], [[3, 2, 4, 1, 5], {4}, {}], [[3, 2, 4, 5, 1], {4}, {}], [[3, 2, 5, 1, 4], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 1, 5], {4}, {}], [[3, 4, 2, 5, 1], {4}, {}], [[3, 5, 2, 1, 4], {1, 4}, {}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 1, 2, 3, 5], {4}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 4}, {}], [[4, 2, 3, 1, 5], {4}, {}], [[4, 2, 3, 5, 1], {4}, {}], [[4, 2, 5, 1, 3], {3, 4}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}], [[4, 5, 2, 1, 3], {1, 4}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {}], [[5, 1, 2, 3, 4], {4}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 4}, {}], [[5, 2, 3, 1, 4], {4}, {}], [[5, 2, 3, 4, 1], {4}, {}], [[5, 2, 4, 1, 3], {3, 4}, {}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 462, 2582, 16214, 113166, 869662, 7299718, 66465126, 652581758, 6873654062, 77319457014, 925138199158, 11732850258670, 157219317318462, 2219625412698470, 32931422398008710] "" "Class ", 133, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 134, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 135, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 392, 1780, 8332, 39924, 194900, 966068, 4849836, 24611244, 126058636, 650910492, 3384968732, 17714233448, 93224854050, 493100610998, 2620131369382] "" "Class ", 136, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2629, 16302, 111150, 826590, 6660771, 57837298, 538622495, 5357460755, 56707646603, 636662827656, 7559228577253, 94662345739833, 1247214995754394, 17250035025108946] "" "Class ", 137, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2366, 13498, 82762, 541314, 3755726, 27523098, 212273362, 1717541850, 14538423670, 128428367338, 1181381455714, 11293984972202, 112009193804494, 1150539748360978] "" "Class ", 138, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {3}, {}], [[1, 5, 3, 4, 2], {3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 3, 4, 1], {1, 3}, {}], [[2, 5, 4, 3, 1], {1, 3}, {}], [[4, 1, 2, 3, 5], {1, 3}, {}], [[4, 1, 3, 2, 5], {1, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {3}, {}], [[5, 1, 3, 4, 2], {3}, {}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 3, 4, 1], {2, 3}, {}], [[5, 2, 4, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 466, 2628, 16528, 114464, 865212, 7085306, 62460820, 589548824, 5930460238, 63324890408, 715240029494, 8518621154446, 106689545641942, 1401611729544236, 19271255642438192] "" "Class ", 139, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 140, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 141, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 368, 1584, 6968, 31192, 141656, 651136, 3023840, 14166496, 66876096, 317809216, 1519163456, 7299577216, 35237444736, 170812433536, 831127053696] "" "Class ", 142, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 143, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 144, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[1, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1840, 8924, 44804, 231420, 1223944, 6604020, 36248316, 201928072, 1139516668, 6504146224, 37501504096, 218186477912, 1279766296464, 7561665704872] "" "Class ", 145, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 2]}], [[2, 1, 3], {3}, {[0, 0, 0, 1]}], [[2, 3, 1], {2}, {[0, 0, 0, 2]}], [[3, 1, 2], {1}, {[0, 0, 0, 2]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 87, 354, 1459, 6056, 25252, 105632, 442916, 1860498, 7826120, 32956964, 138911074, 585926818, 2472923499, 10442263142, 44112331275, 186413949540] "" "Class ", 146, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 565, 3640, 26837, 222517, 2049981, 20775701, 229689323, 2750992340, 35483234077, 490365353223, 7228449666276, 113213834120629, 1877488998499143, 32865209492792707, 605580391308882148] "" "Class ", 147, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 1, 5, 2, 4], {2, 3}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}], [[4, 1, 5, 2, 3], {2, 3}, {}], [[4, 1, 5, 3, 2], {1, 2, 3}, {}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 524, 3169, 21612, 163787, 1364636, 12395795, 121862612, 1288791197, 14586923309, 175897079250, 2250943923286, 30463411423035, 434674441130282, 6521186621466753, 102610213436144210] "" "Class ", 148, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 149, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 150, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 552, 3546, 25968, 214120, 1962432, 19779808, 217480496, 2590622900, 33233242928, 456772189792, 6696626103480, 104313916373440, 1720488407603472, 29953130212324528, 548920121353644464] "" "Class ", 151, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 152, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 153, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 154, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 565, 3650, 26959, 224003, 2067957, 21000531, 232652236, 2792193163, 36088495581, 499752831461, 7381938641252, 115854941129147, 1925228454562192, 33770001251800194, 623528454797269229] "" "Class ", 155, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 156, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 157, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 158, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 549, 3516, 25718, 211636, 1935102, 19462710, 213546149, 2538300206, 32492171727, 445633304822, 6519364852244, 101335561084852, 1667792615115186, 28973656860356055, 529835402050992732] "" "Class ", 159, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 160, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 161, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 162, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]} "Class ", 163, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 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}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {2, 3, 4}, {[1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2508, 14838, 95103, 654420, 4802385, 37383266, 307266259, 2656271284, 24071976552, 228024299869, 2252047004692, 23137951362902, 246804601394039, 2728222558416547] "" "Class ", 164, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 165, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]} "Class ", 166, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2514, 15378, 103762, 765450, 6127270, 52883426, 489443842, 4834644626, 50758956102, 564377967866, 6624274492810, 81840713947706, 1061555216414314, 14422679109495594] "" "Class ", 167, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 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, 6, 22, 94, 454, 2438, 14392, 92560, 643804, 4812912, 38460742, 326955778, 2944304902, 27982823530, 279771881580, 2934059036336, 32193323804104, 368711398430250, 4398649962732388] "" "Class ", 168, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]} "Class ", 169, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "Class ", 170, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "Class ", 171, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 172, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 173, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 174, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 175, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 176, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 177, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 178, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 179, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 180, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 181, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "Class ", 182, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 183, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 184, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 185, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]} "Class ", 186, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 187, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]} "Class ", 188, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 189, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 190, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2826, 17834, 122482, 906172, 7165413, 60178357, 534054388, 4986848557, 48819712958, 499512571379, 5327329082991, 59082220290034, 679951249108539, 8105123077586381] "" "Class ", 191, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2441, 14299, 90489, 613643, 4430891, 33890643, 273418437, 2318303240, 20595117974, 191179413981, 1849997824635, 18622517824421, 194634730430101, 2108499343342433] "" "Class ", 192, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 193, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 194, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2598, 15743, 103261, 726664, 5447243, 43244628, 361864385, 3179223306, 29229323128, 280412965101, 2800138848398, 29041272351597, 312223964342268, 3473603084840425] "" "Class ", 195, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 196, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 197, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 198, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2827, 17825, 122180, 901428, 7104004, 59438021, 525341811, 4884507516, 47605725433, 484875367741, 5147282260223, 56818072226144, 650810006762717, 7721036564092104] "" "Class ", 199, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 200, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 201, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 202, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2552, 15246, 98377, 679386, 4985680, 38658620, 315255360, 2693300683, 24025849259, 223156077911, 2152777967586, 21523114387673, 222581298494939, 2376851150687511] "" "Class ", 203, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 204, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 205, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 206, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 207, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "Class ", 208, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "Class ", 209, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 210, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 211, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 212, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 213, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 214, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 215, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 216, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 217, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "Class ", 218, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 219, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 220, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 221, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 540, 3412, 24632, 200232, 1808200, 17963440, 194665680, 2285380912, 28893994784, 391401421920, 5655423507040, 86823506958400, 1411343976438720, 24216401536093504, 437383794665601920] "" "Class ", 222, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 556, 3566, 26132, 215429, 1973346, 19883909, 218569790, 2602798829, 33379181684, 458642196177, 6722039683010, 104678398122329, 1725983511291786, 30039818953700652, 550344175155723400] "" "Class ", 223, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 548, 3500, 25534, 209568, 1911292, 19174210, 209842488, 2487893564, 31765482058, 434552483182, 6340999015310, 98310992419292, 1613875645893956, 27965278567867986, 510087434555802648] "" "Class ", 224, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 225, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 226, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2540, 15626, 105994, 785958, 6325138, 54907176, 511425284, 5087826926, 53842565626, 603962663246, 7158165556678, 89384005652578, 1172911600292766, 16136298607932164] "" "Class ", 227, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 228, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 229, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 230, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 231, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 232, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 233, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 234, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2664, 16728, 115801, 875915, 7186971, 63580172, 603302871, 6112877191, 65880587896, 752620019559, 9085963310810, 115598024709815, 1546096758005984, 21689558404813704] "" "Class ", 235, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {3}, {}], [[1, 5, 3, 2, 4], {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]}], [[1, 5, 4, 2, 3], {3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 3, 4, 1], {1, 3}, {}], [[2, 5, 4, 3, 1], {1, 3}, {}], [[4, 1, 2, 3, 5], {1, 3}, {}], [[4, 1, 3, 2, 5], {1, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {3}, {}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {3}, {}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 3, 4, 1], {2, 3}, {}], [[5, 2, 4, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 462, 2568, 15914, 108704, 810998, 6558994, 57142460, 533396246, 5310012648, 56148657396, 628400486990, 7420227254178, 92184606362222, 1201880255104934, 16407132291722332] "" "Class ", 236, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 237, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 238, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 239, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 240, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 241, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 242, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 552, 3546, 25972, 214168, 1963080, 19789218, 217609916, 2592462080, 33261020888, 457211085086, 6703877393320, 104439684714588, 1722775333375032, 29996635847819102, 549784984073301640] "" "Class ", 243, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3428, 24774, 201432, 1819830, 18085490, 196073442, 2302873980, 29127713352, 394735146534, 5706028683812, 87637715715704, 1425186586083648, 24464339766911804, 442050278585348430] "" "Class ", 244, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 564, 3638, 26826, 222504, 2050636, 20789024, 229914354, 2754614448, 35541863862, 491340704388, 7245261094702, 113515265789642, 1883120377698110, 32974862437818794, 607805039071468322] "" "Class ", 245, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 246, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 247, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2706, 16970, 117116, 881598, 7185590, 63026126, 591792662, 5921683376, 62897577172, 706686944552, 8373087305664, 104330854513116, 1363741651607126, 18658216233861982] "" "Class ", 248, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 249, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 250, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 251, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 252, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 253, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 254, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 462, 2582, 16189, 112454, 857056, 7113024, 63872399, 617042356, 6381082189, 70332684171, 823069230274, 10191849015794, 133133085364419, 1829569334902703, 26385823433955157] "" "Class ", 255, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2468, 14714, 95678, 673090, 5088284, 41097470, 352920556, 3208655938, 30772061572, 310293780590, 3280409304478, 36266946369436, 418335916742286, 5024246577629136] "" "Class ", 256, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2734, 17260, 119926, 908838, 7456724, 65827782, 621992252, 6261915912, 66905489882, 756033557800, 9007587243330, 112841812839398, 1482697567494930, 20388523732534560] "" "Class ", 257, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 258, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 259, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 260, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 261, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 262, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 263, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 540, 3412, 24632, 200232, 1808200, 17963440, 194665680, 2285380912, 28893994784, 391401421920, 5655423507040, 86823506958400, 1411343976438720, 24216401536093504, 437383794665601920] "" "Class ", 264, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 562, 3644, 27004, 225126, 2085534, 21251568, 236241965, 2845009309, 36897392008, 512708542927, 7599311966519, 119675948395389, 1995552159796632, 35123709533269025, 650749837180587121] "" "Class ", 265, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3416, 24582, 198930, 1788542, 17687736, 190822234, 2230212088, 28070331382, 378540167456, 5445089956542, 83219876698268, 1346705560345526, 23003786705247084, 413620832853767990] "" "Class ", 266, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 267, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 268, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2446, 14542, 94752, 672232, 5164218, 42731772, 379047246, 3588789140, 36126778796, 385322295004, 4340871119260, 51507053900344, 642082025994590, 8389706572116656] "" "Class ", 269, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 270, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 271, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 272, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 273, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 274, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 275, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[1, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {[1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2736, 17302, 120576, 917762, 7574016, 67354582, 642041856, 6530291042, 70589700096, 808090395862, 9766250151936, 124258689304322, 1660195646078976, 23239748527125142] "" "Class ", 276, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2985, 20099, 151232, 1258801, 11487725, 114101915, 1225611465, 14159279213, 175094828970, 2307946603950, 32305698066880, 478621492270914, 7482917449490087, 123125773306628220] "" "Class ", 277, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {3, 4}, {}], [[1, 5, 3, 4, 2], {3, 4}, {}], [[2, 5, 3, 4, 1], {1, 3, 4}, {}], [[4, 1, 3, 2, 5], {1, 3, 4}, {}], [[5, 1, 3, 2, 4], {3, 4}, {}], [[5, 1, 4, 2, 3], {3, 4}, {}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2736, 17302, 120576, 917762, 7574016, 67354582, 642041856, 6530291042, 70589700096, 808090395862, 9766250151936, 124258689304322, 1660195646078976, 23239748527125142] "" "Class ", 278, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 279, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 280, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 281, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 282, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 283, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 284, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 285, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 543, 3438, 24874, 202440, 1830963, 18216809, 197727053, 2324981570, 29441292835, 399445106908, 5780772448620, 88888086707378, 1447187371588622, 24870646852531411, 449910155501687247] "" "Class ", 286, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 287, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 288, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 289, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 545, 3472, 25298, 207396, 1889082, 18926424, 206856144, 2449233930, 31230455685, 426668124740, 6217716278410, 96272105471308, 1578314607893582, 27312896910468616, 497528944555049468] "" "Class ", 290, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 291, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 292, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 293, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 294, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 295, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 296, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} "Class ", 297, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {[0, 1, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2474, 14848, 97734, 700470, 5432394, 45339624, 405285494, 3863600678, 39131692110, 419665074818, 4751140335300, 56627326182388, 708780161189900, 9295560780687234] "" "Class ", 298, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 299, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 300, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 301, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 302, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 303, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 304, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 305, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 306, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 307, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 308, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 309, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 310, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 311, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [3, 2, 4, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 392, 1776, 8272, 39352, 190436, 934824, 4645022, 23323782, 118189674, 603740710, 3106089924, 16081874536, 83740619276, 438300301748, 2304817500484] "" "Class ", 312, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1814, 8712, 43448, 224308, 1195834, 6569410, 37118662, 215344124, 1280810860, 7799179028, 48560427988, 308812221332, 2003726704484, 13252813059496] "" "Class ", 313, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 314, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 315, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 316, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 317, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 318, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 319, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 320, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 321, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 322, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 323, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 324, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 325, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 326, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 327, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 328, " is:" {{[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 329, " is:" {{[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 330, " is:" {{[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 331, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 332, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2732, 17226, 119490, 903730, 7398212, 65152722, 614032600, 6165254754, 65691565454, 740234873774, 8794313085916, 109854804255042, 1439304448291870, 19734969974854664] "" "Class ", 333, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 334, " is:" {{[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 335, " is:" {{[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 336, " is:" {{[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 337, " is:" {{[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 338, " is:" {{[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 339, " is:" {{[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 340, " is:" {{[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 341, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 564, 3620, 26596, 219612, 2014672, 20332536, 223833792, 2669493896, 34286044984, 471809003520, 6925401096568, 108007092471024, 1783541019574104, 31088167274197232, 570405214842714232] "" "Class ", 342, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 535, 3305, 23145, 181213, 1568660, 14876356, 153384716, 1708368364, 20440588242, 261478978286, 3561162460278, 51446182422742, 785768315777656, 12651442259685336, 214161707173871024] "" "Class ", 343, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {3, 4}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {3, 4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 532, 3240, 22272, 170072, 1428612, 13085468, 129738316, 1384045724, 15803634812, 192279482716, 2482960535820, 33912320069132, 488378794886228, 7395524879360300, 117466888771432644] "" "Class ", 344, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 501, 2877, 18259, 126385, 945004, 7573768, 64652306, 584754972, 5579055902, 55937428444, 587461462268, 6443934205994, 73641869521696, 874843053654046, 10782007646430584] "" "Class ", 345, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {2, 3}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 519, 3103, 20863, 155414, 1270577, 11305075, 108703723, 1123093343, 12405051744, 145850191942, 1818422004200, 23960859573149, 332685974771281, 4854338469269119, 74257891310726795] "" "Class ", 346, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 483, 2657, 15908, 102432, 703463, 5118934, 39262595, 316076183, 2661208157, 23363501920, 213329455457, 2021367470121, 19836583500332, 201260116002213, 2107851355277037] "" "Class ", 347, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 497, 2807, 17419, 116999, 843629, 6481949, 52741994, 452319346, 4071392214, 38327882222, 376224452238, 3840420239174, 40672162844587, 445967721752313, 5053508110083617] "" "Class ", 348, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 464, 2416, 13328, 76926, 460675, 2844561, 18024284, 116763122, 771024783, 5177271023, 35281306961, 243604401763, 1701850250439, 12015530629231, 85647134423349] "" "Class ", 349, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3035, 20256, 149880, 1216821, 10752569, 102697938, 1054008038, 11566361053, 135123809269, 1674178008448, 21925515030352, 302607061995377, 4389628314414485, 66764948703957682] "" "Class ", 350, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 2, 4], [1, 1, 0]]} "Class ", 351, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 564, 3632, 26756, 221648, 2040488, 20662916, 228263420, 2731781448, 35207794128, 486178034164, 7161111616660, 112071321017584, 1857086512195624, 32482606269690948, 598061710848213212] "" "Class ", 352, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 535, 3305, 23145, 181213, 1568660, 14876356, 153384716, 1708368364, 20440588242, 261478978286, 3561162460278, 51446182422742, 785768315777656, 12651442259685336, 214161707173871024] "" "Class ", 353, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 354, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 355, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3}, {}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 532, 3244, 22338, 171128, 1443846, 13300076, 132792896, 1428368470, 16465472398, 202491235880, 2646122360424, 36615133727790, 534812759306034, 8222771309996792, 132744101400595332] "" "Class ", 356, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 500, 2858, 17999, 123237, 908675, 7160335, 59930290, 530094596, 4934168945, 48157432591, 491307349222, 5225283602318, 57796437800951, 663455766321947, 7889065799250087] "" "Class ", 357, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 358, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 359, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 557, 3560, 26025, 214103, 1956099, 19660897, 215586269, 2560838043, 32759197374, 449002870931, 6564353801540, 101968094536418, 1677105313199608, 29116374821251410, 532096880231329235] "" "Class ", 360, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3035, 20256, 149880, 1216821, 10752569, 102697938, 1054008038, 11566361053, 135123809269, 1674178008448, 21925515030352, 302607061995377, 4389628314414485, 66764948703957682] "" "Class ", 361, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 362, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 363, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 516, 3112, 21166, 160382, 1338878, 12207098, 120692650, 1286101786, 14692831546, 179140319614, 2321681521094, 31871178179078, 461970377863138, 7050618144834190, 113014620890993482] "" "Class ", 364, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2481, 14401, 89478, 590039, 4102749, 29924867, 227998777, 1808303540, 14886078182, 126875978476, 1117210633580, 10144521239565, 94830883959921, 911276512016136] "" "Class ", 365, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 366, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 367, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 553, 3520, 25615, 209606, 1905798, 19061365, 207976623, 2458334416, 31293357722, 426802160081, 6209118379115, 95975893436988, 1570789460240920, 27136566019993425, 493478449577683425] "" "Class ", 368, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 505, 2951, 19287, 139219, 1100452, 9454648, 87738512, 874781932, 9326725251, 105897576361, 1275788542637, 16254827232201, 218383309674042, 3085579755049630, 45739282428969970] "" "Class ", 369, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 370, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 371, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 526, 3199, 22021, 168852, 1427596, 13193698, 132288769, 1430342456, 16587508051, 205376745669, 2703926298216, 37719014502824, 555738255916054, 8623601710199523, 140573503114061994] "" "Class ", 372, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 477, 2627, 15833, 102983, 716572, 5297372, 41354180, 339358408, 2915738326, 26140494670, 243847915454, 2360834367036, 23669944325728, 245284833323372, 2622577907639100] "" "Class ", 373, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 374, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 375, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 506, 2966, 19464, 141136, 1120818, 9673718, 90159804, 902523148, 9657740246, 110020750430, 1329457487264, 16984901914284, 228757932826310, 3239465599924122, 48119494640056024] "" "Class ", 376, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2648, 16113, 106221, 751938, 5675274, 45384832, 382708150, 3388701378, 31394223754, 303385334378, 3049972823526, 31822152725872, 343865059710724, 3841122099148058] "" "Class ", 377, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 103, 576, 3768, 28126, 236272, 2205328, 22642688, 253611806, 3077302318, 40212239524, 563000285818, 8407908650728, 133412377256348, 2241444186114000, 39750336608060466, 742044736611296280] "" "Class ", 378, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 548, 3445, 24568, 195962, 1727719, 16681521, 175019908, 1982485209, 24109804834, 313300655679, 4332111569138, 63505767226173, 983753254784049, 16056614674103835, 275409992987964036] "" "Class ", 379, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 380, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 381, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 529, 3211, 21927, 166617, 1393078, 12715318, 125792218, 1340838520, 15319444927, 186767863077, 2420102007023, 33213602312579, 481273917538284, 7342529368008344, 117646340650323516] "" "Class ", 382, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 500, 2858, 17999, 123237, 908675, 7160335, 59930290, 530094596, 4934168945, 48157432591, 491307349222, 5225283602318, 57796437800951, 663455766321947, 7889065799250087] "" "Class ", 383, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 384, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 385, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 516, 3112, 21166, 160382, 1338878, 12207098, 120692650, 1286101786, 14692831546, 179140319614, 2321681521094, 31871178179078, 461970377863138, 7050618144834190, 113014620890993482] "" "Class ", 386, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 387, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 555, 3558, 26087, 215068, 1970540, 19858987, 218335766, 2600498900, 33355725952, 458404726828, 6719790002954, 104662599054114, 1726040046828955, 30046320519126605, 550564421266877710] "" "Class ", 388, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3032, 20292, 150672, 1228708, 10911034, 104752354, 1080898810, 11926571964, 140102866628, 1745484713720, 22985421055432, 318971099985028, 4652055230291698, 71134657643300778] "" "Class ", 389, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 390, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 391, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3060, 20689, 155749, 1293562, 11749464, 115846272, 1232555402, 14073796081, 171679073667, 2228180035196, 30658049244876, 445771620649647, 6829697206030137, 109973588344300439] "" "Class ", 392, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 477, 2627, 15833, 102983, 716572, 5297372, 41354180, 339358408, 2915738326, 26140494670, 243847915454, 2360834367036, 23669944325728, 245284833323372, 2622577907639100] "" "Class ", 393, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 394, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 395, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 508, 3006, 19998, 147524, 1194890, 10537330, 100464142, 1029512330, 11282284244, 131646521714, 1629337704790, 21317494458902, 293955324179984, 4260686305938720, 64755847462264812] "" "Class ", 396, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 397, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 553, 3534, 25804, 211949, 1934507, 19421871, 212716087, 2523914264, 32250199957, 441523229321, 6447681641980, 100042024186034, 1643557684186606, 28501553676041928, 520269669818307706] "" "Class ", 398, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 508, 3006, 19998, 147524, 1194890, 10537330, 100464142, 1029512330, 11282284244, 131646521714, 1629337704790, 21317494458902, 293955324179984, 4260686305938720, 64755847462264812] "" "Class ", 399, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 400, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 401, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3054, 20686, 156107, 1298815, 11810735, 116509089, 1239080778, 14131718579, 172043875077, 2226786813350, 30532851324036, 442109289152875, 6741146817252966, 107961986072448432] "" "Class ", 402, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 460, 2453, 14276, 89542, 600381, 4275298, 32154435, 254284387, 2106603295, 18224269317, 164185659628, 1536754818266, 14912467120406, 149749096413290, 1553562656218178] "" "Class ", 403, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 404, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 405, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3127, 21324, 161940, 1354485, 12368855, 122445196, 1306077232, 14932762791, 182176606789, 2362130217700, 32437677513500, 470298276679495, 7178907697047901, 115082120835162814] "" "Class ", 406, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2750, 17309, 119095, 886540, 7081638, 60301040, 544377922, 5186484928, 51946010954, 545107596001, 5975806362575, 68262526616562, 810689090691078, 9989261281819980] "" "Class ", 407, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 558, 3594, 26485, 219391, 2019759, 20453998, 225951874, 2704181143, 34852292602, 481273505090, 7088951860073, 110943017598859, 1838408966666089, 32156232124344748, 592058462805018030] "" "Class ", 408, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3093, 21125, 160807, 1349530, 12376888, 123119268, 1320120122, 15175963209, 186185916453, 2427906971195, 33532557785117, 488965050663556, 7506497468850170, 121015224193974958] "" "Class ", 409, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, {}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3089, 21040, 159512, 1331981, 12139903, 119856699, 1273985725, 14500880936, 175937399758, 2266307282223, 30884720595969, 443890558359268, 6709693514134634, 106398102086361018] "" "Class ", 410, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, {}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 1, 5], {3, 4}, {}], [[3, 2, 4, 5, 1], {3}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {}], [[4, 1, 3, 5, 2], {2}, {}], [[4, 2, 3, 5, 1], {2}, {}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {2, 3}, {}], [[5, 1, 3, 4, 2], {2, 3}, {}], [[5, 2, 3, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2676, 16636, 113098, 832225, 6575939, 55424426, 495558574, 4678884631, 46466130513, 483732832998, 5263400346656, 59702207925241, 704331479733335, 8624492613942410] "" "Class ", 411, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3060, 20689, 155749, 1293562, 11749464, 115846272, 1232555402, 14073796081, 171679073667, 2228180035196, 30658049244876, 445771620649647, 6829697206030137, 109973588344300439] "" "Class ", 412, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 460, 2436, 13957, 85469, 555016, 3799235, 27271012, 204447261, 1595389594, 12921128448, 108349438239, 938689916391, 8386474872242, 77141461626202, 729478280133298] "" "Class ", 413, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, {}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2652, 16179, 106987, 760163, 5759989, 46251036, 391660134, 3482678855, 32402068867, 314451777983, 3174490736905, 33258913031471, 360864325655947, 4047309123283742] "" "Class ", 414, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, {}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 441, 2213, 11743, 65035, 373081, 2204401, 13352681, 82626909, 520860263, 3337047911, 21688232143, 142764261071, 950538563058, 6394153788006, 43414764913742] "" "Class ", 415, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3054, 20686, 156107, 1298815, 11810735, 116509089, 1239080778, 14131718579, 172043875077, 2226786813350, 30532851324036, 442109289152875, 6741146817252966, 107961986072448432] "" "Class ", 416, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 417, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 520, 3151, 21580, 164970, 1390880, 12825123, 128354157, 1385514621, 16045315988, 198419842689, 2609516222590, 36367209168394, 535362234519884, 8301029951941835, 135221068564789238] "" "Class ", 418, " is:" {{[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]} "Class ", 419, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 3, 4], [1, 0, 0]]}, {[[4, 3, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 3, 4], [1, 0, 0]]}, {[[4, 3, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {}], [[1, 3, 5, 4, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 3, 5, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 558, 3379, 22950, 172660, 1424932, 12797611, 124255356, 1296898666, 14480940583, 172247835393, 2174522289423, 29039906282237, 409041495213172, 6060768847735249, 94239449041139507] "" "Class ", 420, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 3, 4], [1, 0, 0]]}, {[[4, 3, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 3, 4], [1, 0, 0]]}, {[[4, 3, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {}], [[1, 3, 5, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {4}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {4}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 3, 5, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2, 4}, {}], [[2, 5, 3, 4, 1], {2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 103, 524, 2969, 18471, 124790, 907805, 7063118, 58451201, 512122059, 4731721748, 45945232059, 467442556620, 4969598053709, 55078343689085, 634997607721169, 7600613456150852] "" "Class ", 421, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 535, 3305, 23145, 181213, 1568660, 14876356, 153384716, 1708368364, 20440588242, 261478978286, 3561162460278, 51446182422742, 785768315777656, 12651442259685336, 214161707173871024] "" "Class ", 422, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3058, 20750, 157506, 1322686, 12183122, 122146926, 1324518754, 15447439646, 192831941490, 2565512387278, 36241715197058, 541784844462462, 8545264289709202, 141817846453739822] "" "Class ", 423, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 507, 2991, 19759, 144425, 1156012, 10051388, 94289278, 948841364, 10192614320, 116384873470, 1407382891768, 17964280631478, 241336554532194, 3403446075903860, 50266215869515928] "" "Class ", 424, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2666, 16382, 109658, 792258, 6133096, 50565974, 441789094, 4072767230, 39471410430, 400869564178, 4254318048948, 47063346080066, 541500194369378, 6467159564812270] "" "Class ", 425, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 493, 2834, 18106, 127057, 969709, 7986932, 70533154, 664237695, 6639822090, 70170618098, 781277671215, 9136375247763, 111912544875056, 1432399289142591, 19115296812033057] "" "Class ", 426, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 460, 2450, 14134, 87475, 576403, 4020516, 29547043, 227903048, 1838987266, 15480666740, 135621760658, 1233870904415, 11635493511429, 113536009236905, 1144581301853570] "" "Class ", 427, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {2, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2, 4}, {}], [[2, 5, 3, 4, 1], {2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 473, 2583, 15338, 97920, 665636, 4783748, 36133702, 285501518, 2350365402, 20093003446, 177869540892, 1626446139238, 15329653007365, 148650210544983, 1480539591729511] "" "Class ", 428, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 442, 2228, 11816, 65189, 371126, 2167862, 12937275, 78619840, 485268940, 3035997927, 19220474809, 122962692858, 794020019536, 5170337829216, 33921804239139] "" "Class ", 429, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3164, 21592, 163893, 1369345, 12485935, 123354917, 1312469361, 14960945232, 181889117845, 2349181799886, 32119831826139, 463476941293825, 7038389788564931, 112207124143937411] "" "Class ", 430, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2730, 17172, 118520, 889116, 7194004, 62383568, 576677816, 5656891176, 58653066696, 640584346608, 7347121283680, 88255946135376, 1107672668696048, 14493714457542656] "" "Class ", 431, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [0, 1, 0]]} "Class ", 432, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [1, 1, 0]]} "Class ", 433, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2816, 17895, 124701, 944019, 7702956, 67321884, 626828603, 6189588775, 64564216766, 709013561668, 8172304062061, 98606146554266, 1242507993153402, 16315521196770039] "" "Class ", 434, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2492, 14574, 91544, 612258, 4330278, 32211795, 250895245, 2038622810, 17226019243, 150962216287, 1368909554516, 12817943135192, 123713438571246, 1228781053005792] "" "Class ", 435, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [0, 1, 1]]} "Class ", 436, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 2, 4], [1, 1, 1]]} "Class ", 437, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 535, 3311, 23230, 182301, 1581753, 15035986, 155388388, 1734579098, 20799342127, 266627109553, 3638628793029, 52667875733187, 805940890226437, 12999766942475271, 220443088218645306] "" "Class ", 438, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3058, 20750, 157506, 1322686, 12183122, 122146926, 1324518754, 15447439646, 192831941490, 2565512387278, 36241715197058, 541784844462462, 8545264289709202, 141817846453739822] "" "Class ", 439, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 440, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 441, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 505, 2962, 19445, 141218, 1123774, 9722825, 90865181, 912190291, 9789872739, 111855659843, 1355594024358, 17368890460815, 234593001071332, 3331312302008695, 49617905999661764] "" "Class ", 442, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2634, 15998, 105506, 748854, 5680988, 45800112, 390522730, 3507441762, 33065146414, 326176916006, 3357886214968, 35988919087196, 400712987218258, 4626219200283254] "" "Class ", 443, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 444, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 445, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3097, 21097, 160275, 1343386, 12312989, 122498017, 1314539355, 15134201164, 186064105788, 2432828777517, 33708807056863, 493365448679488, 7605787680674682, 123182917413559210] "" "Class ", 446, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2595, 15869, 106058, 767920, 5980511, 49798605, 441125321, 4139020575, 40982689862, 426825241902, 4662221457571, 53273830905925, 635352701351188, 7892171199064181] "" "Class ", 447, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 448, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 449, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 475, 2695, 17088, 119779, 920077, 7688321, 69453940, 674664072, 7014021800, 77721146283, 914548779303, 11390460389988, 149712002325129, 2071047879626380, 30080545102294073] "" "Class ", 450, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 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]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2124, 11331, 63908, 378389, 2339073, 15031192, 100060707, 688009341, 4874454871, 35510359415, 265522418872, 2034622239216, 15955245479023, 127887548234220] "" "Class ", 451, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 452, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 453, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3046, 20498, 153554, 1266604, 11407099, 111349312, 1170957196, 13196245589, 158652613915, 2026759482225, 27415209815967, 391433602974194, 5882841898304214, 92829097449902643] "" "Class ", 454, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2505, 14807, 94767, 651496, 4784063, 37341413, 308591988, 2690718638, 24679087232, 237457399382, 2390974142131, 25137909150009, 275401451770529, 3138188254909177] "" "Class ", 455, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 456, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 457, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2772, 17666, 124067, 951479, 7908637, 70804597, 679168630, 6948199858, 75512839640, 868771425312, 10548214906213, 134783270797142, 1807972078830363, 25401771851457663] "" "Class ", 458, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2259, 12507, 73669, 458250, 2991383, 20396271, 144676702, 1064176199, 8094463876, 63519121275, 513184454461, 4261117914981, 36305391518985, 316964839475016] "" "Class ", 459, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 460, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 461, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 527, 3232, 22476, 174796, 1503320, 14168945, 145236077, 1608621710, 19145473758, 243681030090, 3302875087332, 47496771973889, 722276867909535, 11580528086332168, 195246833999413604] "" "Class ", 462, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2730, 17172, 118520, 889116, 7194004, 62383568, 576677816, 5656891176, 58653066696, 640584346608, 7347121283680, 88255946135376, 1107672668696048, 14493714457542656] "" "Class ", 463, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2876, 18631, 133190, 1040888, 8824332, 80636308, 789951438, 8258055977, 91750982113, 1079595105871, 13411073903650, 175387693774798, 2408627656714074, 34656220504980788] "" "Class ", 464, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2509, 14786, 93888, 636826, 4582302, 34784691, 277290033, 2312301886, 20104290424, 181732877733, 1703743725811, 16529367265570, 165635052801014, 1711375540674625] "" "Class ", 465, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2964, 19815, 147857, 1219928, 11036431, 108715957, 1158869975, 13296004508, 163409827238, 2142266385276, 29844766182310, 440348267871950, 6860206120714237, 112537690142138675] "" "Class ", 466, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2411, 13963, 87042, 579259, 4088943, 30457287, 238374743, 1953283669, 16706473009, 148757363759, 1375787882351, 13189453993725, 130835235093995, 1340746108292891] "" "Class ", 467, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 5, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2573, 15558, 102310, 725428, 5507849, 44526476, 381447272, 3448763031, 32792399537, 326904635695, 3407360955235, 37042780208555, 419106608480448, 4925158252128654] "" "Class ", 468, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 434, 2180, 11592, 64507, 372564, 2219474, 13573425, 84898175, 541477929, 3513044190, 23138725575, 154463183169, 1043592235288, 7127523758903, 49159095871710] "" "Class ", 469, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3060, 20576, 153656, 1260988, 11276044, 109096136, 1135211856, 12639705168, 149922271336, 1887039463848, 25118637765808, 352525315583696, 5202127455196216, 80519833130609864] "" "Class ", 470, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2548, 15307, 99982, 704364, 5317229, 42783966, 365277342, 3296368737, 31336785031, 312887691172, 3272563656187, 35770313198136, 407720584972148, 4836874784178147] "" "Class ", 471, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 475, 2673, 16686, 114216, 849289, 6809139, 58501108, 535830309, 5209140432, 53546709749, 580078872669, 6603331690283, 78783594614393, 982878754087217, 12795287909946861] "" "Class ", 472, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2283, 12806, 76887, 490140, 3297237, 23287666, 171966446, 1323027488, 10573150101, 87543547498, 749293089085, 6616459746684, 60170690042155, 562664473935604] "" "Class ", 473, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2588, 15720, 103937, 741382, 5665954, 46127245, 398147779, 3628863615, 34804087109, 350189568390, 3686626904312, 40511225829775, 463678627436942, 5517224165253576] "" "Class ", 474, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 475, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 3}, {}], [[5, 1, 3, 4, 2], {1, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 443, 2327, 13248, 80948, 525900, 3609537, 26025259, 196250943, 1541874885, 12581323746, 106328837684, 928522450132, 8360810517272, 77485983505489, 737922217948914] "" "Class ", 476, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 477, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 534, 3271, 22652, 174653, 1484126, 13777225, 138692791, 1504836269, 17505050027, 217314085754, 2867614694708, 40079604415639, 591463296248956, 9189855397725993, 149955564904878524] "" "Class ", 478, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2948, 19468, 142536, 1145054, 10011760, 94627066, 961201586, 10441276956, 120769417766, 1481764208064, 19220564264696, 262797966217640, 3777325930373024, 56938393801915768] "" "Class ", 479, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]} "Class ", 480, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]} "Class ", 481, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2816, 17895, 124701, 944019, 7702956, 67321884, 626828603, 6189588775, 64564216766, 709013561668, 8172304062061, 98606146554266, 1242507993153402, 16315521196770039] "" "Class ", 482, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 451, 2373, 13488, 81903, 526982, 3570181, 25339653, 187654481, 1445108991, 11539669456, 95320338266, 812771130804, 7140810231834, 64539130788912, 599201066502367] "" "Class ", 483, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]} "Class ", 484, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]} "Class ", 485, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 546, 3423, 24283, 192683, 1688863, 16211432, 169076968, 1903925287, 23019675778, 297426834107, 4089591473183, 59622521850589, 918662603266162, 14916047767793375, 254545821120810099] "" "Class ", 486, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 522, 3175, 21836, 167796, 1424504, 13247389, 133941774, 1463255901, 17178079006, 215692500660, 2884669067338, 40941442959519, 614628685301922, 9731263640463595, 162062038298266616] "" "Class ", 487, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 488, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 489, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 503, 2939, 19197, 138726, 1098729, 9464114, 88095821, 881214276, 9427031891, 107399393257, 1298207289717, 16594548183223, 223655720677333, 3169797716463919, 47127497537452843] "" "Class ", 490, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2634, 15998, 105506, 748854, 5680988, 45800112, 390522730, 3507441762, 33065146414, 326176916006, 3357886214968, 35988919087196, 400712987218258, 4626219200283254] "" "Class ", 491, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 492, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 493, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 518, 3156, 21754, 167427, 1422946, 13233199, 133660395, 1456944151, 17046072316, 213059983029, 2833260616501, 39939299587402, 594896164175275, 9335853065813096, 153960646706944865] "" "Class ", 494, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 476, 2715, 17354, 122864, 954457, 8072288, 73837838, 726355814, 7646882726, 85788158186, 1021740841496, 12875674085477, 171164614382037, 2393879753114626, 35137952429145728] "" "Class ", 495, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 496, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 497, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 475, 2695, 17088, 119779, 920077, 7688321, 69453940, 674664072, 7014021800, 77721146283, 914548779303, 11390460389988, 149712002325129, 2071047879626380, 30080545102294073] "" "Class ", 498, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 499, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 500, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 501, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3098, 21174, 161521, 1359788, 12520747, 125159540, 1349677798, 15616552162, 192973328814, 2536249101199, 35326632861763, 519800389998257, 8056551131312778, 131195486106351325] "" "Class ", 502, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2613, 16108, 108857, 799344, 6330069, 53725964, 486138842, 4668439014, 47392817390, 506864437620, 5693683872870, 66995767458058, 823772040436210, 10561613197216045] "" "Class ", 503, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 504, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 505, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2636, 16453, 113268, 852703, 6966369, 61381697, 580118873, 5853729920, 62805651147, 713945365867, 8571123084388, 108363820051614, 1439083458986269, 20028049424982557] "" "Class ", 506, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 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], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {1, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2259, 12507, 73669, 458250, 2991383, 20396271, 144676702, 1064176199, 8094463876, 63519121275, 513184454461, 4261117914981, 36305391518985, 316964839475016] "" "Class ", 507, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 508, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 509, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 530, 3265, 22824, 178447, 1542590, 14610389, 150463910, 1673942705, 20007231030, 255673975989, 3478705985652, 50208050833637, 766171075581876, 12325305445493707, 208468367060538452] "" "Class ", 510, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2948, 19468, 142536, 1145054, 10011760, 94627066, 961201586, 10441276956, 120769417766, 1481764208064, 19220564264696, 262797966217640, 3777325930373024, 56938393801915768] "" "Class ", 511, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]} "Class ", 512, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]} "Class ", 513, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2964, 19815, 147857, 1219928, 11036431, 108715957, 1158869975, 13296004508, 163409827238, 2142266385276, 29844766182310, 440348267871950, 6860206120714237, 112537690142138675] "" "Class ", 514, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2588, 15713, 103741, 738002, 5615595, 45431921, 388852291, 3506162884, 33184212610, 328640320648, 3396316752324, 36537739251620, 408306211871901, 4730465526016739] "" "Class ", 515, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]} "Class ", 516, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]} "Class ", 517, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 516, 3116, 21249, 161226, 1347252, 12289303, 121496889, 1293867298, 14764774667, 179721885388, 2324264957315, 31824147714023, 459895332758550, 6994857811423981, 111692383677165542] "" "Class ", 518, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 95, 471, 2622, 16172, 109186, 799706, 6306844, 53226910, 478242948, 4554505536, 45798753232, 484659172666, 5381616120792, 62538545541570, 758798447616406, 9592572016736790] "" "Class ", 519, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 520, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 521, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2627, 16235, 109937, 808083, 6399907, 54272630, 490239067, 4695801239, 47512274704, 506090682045, 5658262063100, 66224784732987, 809492117024365, 10311790523260605] "" "Class ", 522, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 523, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 524, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 525, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3098, 21011, 158524, 1316478, 11929915, 117132496, 1238487865, 14029060464, 169484003776, 2175100734259, 29550568305060, 423683072579756, 6392901989477881, 101262628412743432] "" "Class ", 526, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 488, 2818, 18188, 129670, 1011348, 8560934, 78135184, 764647014, 7985276380, 88620280354, 1041387188272, 12916108088562, 168596294876412, 2310181511972790, 33152767107991672] "" "Class ", 527, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} "Class ", 528, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} "Class ", 529, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2606, 15945, 106509, 769506, 5971870, 49479164, 435534502, 4055436318, 39799739001, 410351331657, 4432414191241, 50032199729490, 588860940974609, 7212054259731327] "" "Class ", 530, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2317, 13168, 80333, 521571, 3580793, 25857819, 195552235, 1543189011, 12668176280, 107893707121, 951173177239, 8662101591546, 81340443301515, 786345013574944] "" "Class ", 531, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} "Class ", 532, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} "Class ", 533, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3107, 21191, 160865, 1345725, 12294251, 121771750, 1299610082, 14866124523, 181434261494, 2353082624433, 32316125506655, 468492145412371, 7149347263024459, 114554758104645199] "" "Class ", 534, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[1, 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, 6, 22, 95, 471, 2622, 16172, 109186, 799706, 6306844, 53226910, 478242948, 4554505536, 45798753232, 484659172666, 5381616120792, 62538545541570, 758798447616406, 9592572016736790] "" "Class ", 535, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 536, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 537, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2693, 17138, 120699, 932225, 7835143, 71200057, 695690572, 7273884058, 81041579023, 958579508516, 11997525060200, 158420843858754, 2201052802650271, 32099284062809602] "" "Class ", 538, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[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], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2140, 11613, 67425, 416290, 2720279, 18739332, 135636443, 1028555208, 8150828753, 67345156865, 578952088728, 5168814299028, 47841013067828, 458332325362223] "" "Class ", 539, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 540, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 541, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 524, 3239, 22687, 177651, 1537655, 14574946, 150128895, 1669692683, 19939829546, 254477382876, 3456274171523, 49774209189805, 757567718425563, 12150489679678127, 204824942072135539] "" "Class ", 542, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 479, 2756, 17794, 127406, 1001626, 8576597, 79441334, 791376592, 8436420596, 95825855103, 1155312093317, 14734641099882, 198195495857075, 2804055311457415, 41625250882649899] "" "Class ", 543, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 478, 2756, 17923, 129799, 1036124, 9039459, 85575508, 873717499, 9569929255, 111933326697, 1392395847603, 18355242804460, 255601059570476, 3749081673644056, 57772908862792165] "" "Class ", 544, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 446, 2393, 14178, 91736, 642401, 4832743, 38815645, 331101160, 2986062431, 28361579157, 282736129185, 2949556007469, 32115200059434, 364101791052365, 4289226463707934] "" "Class ", 545, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 476, 2716, 17385, 123388, 961621, 8164126, 74999620, 741222356, 7841815497, 88424961854, 1058673407104, 13412331574115, 179260969153276, 2520718347830016, 37200801536720138] "" "Class ", 546, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 547, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {2, 3}, {}], [[1, 2, 5, 3, 4], {2, 3}, {}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 443, 2346, 13667, 86802, 596346, 4401774, 34702711, 290732519, 2576899420, 24071227089, 236169433168, 2426461348334, 26037048707104, 291102726606111, 3383837013821585] "" "Class ", 548, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 549, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3144, 21691, 166998, 1420746, 13227141, 133786362, 1460539197, 17117147227, 214336393961, 2855751450737, 40338249546805, 602118153773490, 9470104077809412, 156532539091428698] "" "Class ", 550, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 475, 2712, 17421, 124177, 972574, 8301328, 76686507, 762224188, 8110391304, 91978020942, 1107469005448, 14109097128099, 189610944460014, 2680630630631435, 39769405174100875] "" "Class ", 551, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 1, 2, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2667, 16895, 118495, 911711, 7631832, 69046336, 671223919, 6976874740, 77202852449, 906013550859, 11238266715577, 146900602356926, 2018072410246951, 29065914617957430] "" "Class ", 552, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [3, 5, 1, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2322, 13527, 86004, 591599, 4370805, 34474285, 288793704, 2558092121, 23867889489, 233789623006, 2396997935763, 25656910998134, 286036024282978, 3314408616855800] "" "Class ", 553, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2636, 16453, 113268, 852703, 6966369, 61381697, 580118873, 5853729920, 62805651147, 713945365867, 8571123084388, 108363820051614, 1439083458986269, 20028049424982557] "" "Class ", 554, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 4, 2], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [2, 5, 3, 4, 1], {1, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 4, 2], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2080, 10892, 60078, 346949, 2087458, 13034991, 84208222, 561316555, 3852079409, 27163514061, 196497031681, 1456038734327, 11037641053474, 85500213499489] "" "Class ", 555, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 3}, {}], [[2, 1, 4, 5, 3], {1, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 3}, {}], [[3, 1, 4, 5, 2], {1, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 3}, {}], [[4, 1, 3, 5, 2], {1, 3}, {}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 3}, {}], [[5, 1, 3, 4, 2], {1, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2245, 12451, 73822, 464487, 3082120, 21463107, 156186173, 1183593200, 9311807628, 75862924572, 638537643054, 5541840915399, 49505726320127, 454482967450685] "" "Class ", 556, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 4, 2], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 3}, {}], [[2, 1, 4, 5, 3], {1, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 5, 3, 4, 1], {1, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 3}, {}], [[3, 1, 4, 5, 2], {1, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 3}, {}], [[4, 1, 3, 5, 2], {1, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 4, 2], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 403, 1874, 9046, 44972, 229047, 1190247, 6291806, 33751822, 183393248, 1007769878, 5593459872, 31324123438, 176834716322, 1005573988153, 5756159988396] "" "Class ", 557, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 538, 3365, 23892, 189900, 1668831, 16067492, 168152920, 1900465051, 23066307836, 299205374366, 4130537544664, 60462276437456, 935359548944194, 15248148586882471, 261250490576057496] "" "Class ", 558, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2843, 18386, 131732, 1035568, 8861703, 82008985, 816038605, 8688405886, 98555261023, 1186548661341, 15111251602322, 202965040708720, 2867332168219737, 42502398284952461] "" "Class ", 559, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 560, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 561, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3058, 20750, 157506, 1322686, 12183122, 122146926, 1324518754, 15447439646, 192831941490, 2565512387278, 36241715197058, 541784844462462, 8545264289709202, 141817846453739822] "" "Class ", 562, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2506, 14853, 95504, 661007, 4893662, 38545789, 321543973, 2829346352, 26169015504, 253625229346, 2568606542073, 27115983021081, 297719393141002, 3392880590749283] "" "Class ", 563, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 564, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 565, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 509, 3033, 20373, 152444, 1256682, 11317088, 110531822, 1163666055, 13136228261, 158280824868, 2027500357715, 27512514321821, 394245666804304, 5948999221081126, 94287807488208653] "" "Class ", 566, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2632, 16548, 115380, 883804, 7379367, 66715599, 649337893, 6769776297, 75272338275, 889149319141, 11119914800464, 146785591746251, 2039497449807735, 29753557732273391] "" "Class ", 567, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 568, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 569, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2554, 15409, 101354, 720833, 5507437, 44956938, 390257200, 3588006047, 34814615198, 355395765213, 3806179697882, 42658211943030, 499194234368265, 6086950691064918] "" "Class ", 570, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 421, 2081, 11007, 62079, 372392, 2371080, 15983960, 113748241, 851825035, 6691613212, 54978480775, 471148270221, 4201160763649, 38894377964776, 373139228006857] "" "Class ", 571, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 572, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 573, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3070, 20859, 158216, 1324488, 12130347, 120629545, 1294432842, 14906944063, 183380830048, 2399875311131, 33290776900944, 487932585744728, 7534361529301467, 122252212368511045] "" "Class ", 574, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2595, 16031, 109215, 813822, 6583858, 57471818, 538394203, 5387618975, 57353373417, 647171743523, 7715744222082, 96913568183032, 1279120904105596, 17698656599348176] "" "Class ", 575, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 576, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 577, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2599, 15948, 107243, 783540, 6176160, 52206154, 470795061, 4509308401, 45694300543, 488200682840, 5482737568377, 64547567106734, 794669137331442, 10208465145091606] "" "Class ", 578, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2219, 12094, 70023, 427661, 2741790, 18375962, 128312123, 930739577, 6996124221, 54375402924, 436150605686, 3604265076046, 30639641969649, 267572581053866] "" "Class ", 579, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 580, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 581, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3054, 20669, 156125, 1300882, 11851444, 117188406, 1249767011, 14298092034, 174668310234, 2269183128393, 31238189554470, 454231536417904, 6956703503813697, 111930326157370545] "" "Class ", 582, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2632, 16548, 115380, 883804, 7379367, 66715599, 649337893, 6769776297, 75272338275, 889149319141, 11119914800464, 146785591746251, 2039497449807735, 29753557732273391] "" "Class ", 583, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]} "Class ", 584, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 585, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2638, 16559, 115167, 879921, 7328582, 66098236, 641910284, 6678847621, 74125603753, 874162370490, 10916330784038, 143907733368963, 1997152672251710, 29105209273809082] "" "Class ", 586, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[1, 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, 6, 22, 93, 438, 2277, 12916, 79377, 524989, 3715536, 27997412, 223622884, 1885878918, 16733929338, 155746788535, 1516242967531, 15401421112592, 162860330984033, 1789145161948040] "" "Class ", 587, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]} "Class ", 588, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 589, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3115, 21422, 164764, 1400581, 13037960, 131881366, 1440244534, 16887221245, 211583769926, 2820960258870, 39875911983066, 595673838076861, 9376212317286188, 155106750365205310] "" "Class ", 590, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2595, 16031, 109215, 813822, 6583858, 57471818, 538394203, 5387618975, 57353373417, 647171743523, 7715744222082, 96913568183032, 1279120904105596, 17698656599348176] "" "Class ", 591, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2624, 16421, 113815, 865628, 7168200, 64195219, 618162394, 6368364785, 69884077275, 813726712162, 10019512035616, 130064765395409, 1775137936193204, 25409401479836772] "" "Class ", 592, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 434, 2205, 12052, 70310, 434724, 2832871, 19361822, 138240723, 1027510386, 7927164469, 63315291750, 522378785177, 4443095280011, 38890838225848, 349774358697700] "" "Class ", 593, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2626, 16464, 114525, 876185, 7315833, 66205144, 645523483, 6746730869, 75245831897, 891983470223, 11199262468099, 148462792008545, 2072138139356477, 30373139091021972] "" "Class ", 594, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 416, 1995, 10006, 52178, 282219, 1582504, 9191709, 55240232, 342943165, 2195609839, 14470399171, 98011407150, 681183954859, 4851042508924, 35353533528873] "" "Class ", 595, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 4, 1, 5], {3, 4}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 434, 2223, 12424, 75420, 494775, 3490036, 26339561, 211702545, 1804377008, 16245442079, 153966604578, 1531277542110, 15936485267701, 173118066682426, 1958438376579053] "" "Class ", 596, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 397, 1790, 8258, 38846, 186037, 906812, 4497173, 22677755, 116169949, 603866268, 3181477011, 16968867542, 91524247478, 498702635461, 2742682539879] "" "Class ", 597, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}], [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 3, 1, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [5, 4, 1, 2, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2525, 15195, 100087, 715737, 5521446, 45680164, 403350716, 3784865762, 37602444260, 394222955708, 4348676513237, 50340749172701, 610105386906147, 7724731371949492] "" "Class ", 598, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {[1, 0, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {[1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {3}, {[1, 0, 0, 0, 0]}], [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 3, 1, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 428, 2124, 11258, 63430, 377633, 2365529, 15520977, 106314038, 757717210, 5604533018, 42914335858, 339472285679, 2768860843140, 23247490618659, 200611346654100] "" "Class ", 599, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[1, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 427, 2096, 10854, 58864, 332711, 1955040, 11913730, 75163185, 489970987, 3295276226, 22825360263, 162616295693, 1189812035727, 8929920820948, 68661595877379] "" "Class ", 600, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]} "Class ", 601, " is:" {{[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}} {[[1, 2, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]} "Class ", 602, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 534, 3270, 22616, 174026, 1474278, 13629506, 136495752, 1471722578, 16994443294, 209208998630, 2734732841796, 37825468248102, 551865404293102, 8469337514356802, 136377512457268184] "" "Class ", 603, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 509, 3021, 20149, 149153, 1213224, 10755570, 103216446, 1066040922, 11790851644, 139052460818, 1741875345726, 23098827026484, 323283056443822, 4762267025565960, 73656751757894960] "" "Class ", 604, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 508, 3004, 19916, 146196, 1176184, 10285952, 97110136, 984055600, 10650151184, 122576202840, 1494643584256, 19244579125592, 260877315044032, 3713412963259768, 55371353528807696] "" "Class ", 605, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2705, 16799, 113809, 833110, 6539444, 54698372, 484995516, 4538513884, 44653841990, 460414303856, 4960633167622, 55708793664726, 650625055350856, 7886476216592946] "" "Class ", 606, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [ [1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [ [2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [ [3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [ [4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 491, 2801, 17713, 122637, 920885, 7440928, 64289512, 590773101, 5747825184, 58978861099, 636103721540, 7189648396778, 84936347393557, 1046329353821353, 13412811248357320] "" "Class ", 607, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 608, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 609, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 445, 2265, 12174, 68294, 396649, 2371057, 14522676, 90825130, 578381059, 3741908559, 24549307421, 163073160391, 1095364959016, 7431709106908, 50881599316916] "" "Class ", 610, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]} "Class ", 611, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 1, 0]]} "Class ", 612, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {3}, {}], [[1, 3, 5, 4, 2], {3, 4}, {}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3}, {}], [[2, 3, 5, 4, 1], {3, 4}, {}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3110, 21212, 161184, 1349581, 12340264, 122313777, 1305978718, 14941225176, 182313873349, 2363115116947, 32421901541867, 469364806926450, 7149512734437234, 114297054091249620] "" "Class ", 613, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 488, 2840, 18636, 136180, 1096776, 9652448, 92156968, 948660936, 10473172472, 123430666352, 1546625774272, 20530943209424, 287812247853552, 4248602931388608, 65872252731068608] "" "Class ", 614, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 615, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 616, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 488, 2818, 18193, 129792, 1013280, 8588598, 78521868, 770055599, 8062109428, 89737888783, 1058104485120, 13173871824618, 172698363544331, 2377594289576545, 34296911690967479] "" "Class ", 617, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 618, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 619, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 620, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 621, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 622, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 623, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 624, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 625, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2127, 11378, 64420, 383184, 2380755, 15379449, 102909959, 711078605, 5060466247, 37009611940, 277627623421, 2132636421715, 16751273561232, 134369351462612] "" "Class ", 626, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 627, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 628, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 629, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 630, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 631, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 632, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 633, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 429, 2174, 11828, 68365, 416682, 2662484, 17751877, 123035196, 883609753, 6558092199, 50186022932, 395197899048, 3196818902233, 26523294227075, 225398379177587] "" "Class ", 634, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 635, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 636, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [ [3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2472, 14684, 94670, 656953, 4872351, 38403798, 320165812, 2811873377, 25926442502, 250217889996, 2521092956944, 26457709190917, 288614567959193, 3266547866826833] "" "Class ", 637, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 638, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {3}, {}], [[1, 3, 5, 4, 2], {3, 4}, {}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3}, {}], [[2, 3, 5, 4, 1], {3, 4}, {}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3209, 22146, 170238, 1441474, 13325413, 133486680, 1440015890, 16639943153, 205017933162, 2682511261440, 37141896212017, 542494788971799, 8335227469484288, 134379854085556215] "" "Class ", 639, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[1, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {[1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2939, 19493, 143780, 1167366, 10345514, 99371011, 1028287239, 11404127421, 134939956385, 1696785154804, 22594140663218, 317605651276886, 4699861636973443, 73027618926041675] "" "Class ", 640, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 641, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 642, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {}], [ [3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2782, 17849, 126611, 983650, 8304767, 75696125, 740695296, 7743203165, 86115903434, 1015118009268, 12641346995779, 165821725637642, 2285172343248370, 33006198787846508] "" "Class ", 643, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 5, 4, 2], {4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 5, 4, 1], {4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {4}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2460, 14544, 93224, 642384, 4726360, 36922736, 304832688, 2649109376, 24150115264, 230262171488, 2290183874848, 23705693525376, 254840434430784, 2839932014269184] "" "Class ", 644, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 645, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 646, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 647, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 648, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]} "Class ", 649, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]} "Class ", 650, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 651, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 652, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 3, 5, 4, 1], {3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2474, 14860, 97856, 700844, 5420274, 44998845, 398943619, 3760349587, 37537388249, 395498140438, 4384899505754, 51020580751356, 621520499993948, 7909470363767704] "" "Class ", 653, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {4}, {}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {}], [[1, 4, 5, 3, 2], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {4}, {}], [[2, 3, 5, 4, 1], {3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {}], [[2, 4, 5, 3, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {}], [[3, 4, 5, 2, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {1}, {[0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2138, 11497, 65619, 394793, 2490011, 16389958, 112175898, 795812979, 5836686829, 44154219807, 343848529767, 2751644927541, 22593170666135, 190074059330329] "" "Class ", 654, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 655, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 656, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [ [2, 3, 4, 1, 5], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2466, 14660, 94821, 661634, 4946752, 39406213, 332876217, 2969709258, 27882496647, 274664711131, 2831075479375, 30460119938250, 341355772536148, 3976811483763725] "" "Class ", 657, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 658, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {3, 4}, {}], [[1, 3, 4, 2, 5], {3}, {}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 2, 5, 3], {3}, {}], [[1, 4, 3, 2, 5], {3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3, 4}, {}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 1, 5, 3], {3}, {}], [[2, 4, 3, 1, 5], {3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 1, 5, 2], {3}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2951, 19615, 144833, 1175535, 10398485, 99529505, 1024592381, 11285497046, 132408172522, 1648285194877, 21695703010589, 301027751301031, 4390753032483543, 67158153536229786] "" "Class ", 659, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2493, 14959, 97865, 692033, 5252348, 42536761, 365783427, 3325855121, 31858144595, 320474057438, 3375989912092, 37150250272342, 426093725138374, 5083449682711138] "" "Class ", 660, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 661, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 662, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [ [2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2509, 15391, 104413, 776776, 6289809, 55074084, 518565249, 5225042934, 56097567863, 639325510060, 7708352103109, 98028831346210, 1311359504052181, 18407766798093227] "" "Class ", 663, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 4, 2], {4}, {}], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [ [2, 3, 5, 1, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 4, 1], {4}, {}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {4}, {}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 4}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1982, 10214, 55896, 323751, 1978353, 12715811, 85724400, 604580267, 4449993342, 34109926985, 271746694939, 2246119975882, 19229964138158, 170275855494272] "" "Class ", 664, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 665, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 666, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 667, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} "Class ", 668, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]} "Class ", 669, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]} "Class ", 670, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]} "Class ", 671, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]} "Class ", 672, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 1, 0, 0]}], [[1, 3, 5, 4, 2], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [2, 3, 5, 4, 1], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2468, 14743, 96320, 683080, 5223863, 42838830, 374871531, 3485673989, 34311013724, 356369441439, 3894226790203, 44654498692767, 536060534386669, 6722741441953031] "" "Class ", 673, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {1}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {4}, {}], [[1, 3, 5, 4, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {4}, {}], [ [2, 3, 5, 4, 1], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {}], [[3, 4, 5, 2, 1], {4}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 4, 2], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 405, 1890, 9136, 45490, 232582, 1218343, 6527036, 35707285, 199216706, 1132216206, 6548367124, 38507944117, 230056905725, 1395326949407, 8585979517162] "" "Class ", 674, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {3}, {}], [[1, 3, 5, 4, 2], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1}, {}], [[2, 1, 4, 5, 3], {1, 4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3}, {}], [[2, 3, 5, 4, 1], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1}, {}], [[3, 1, 4, 5, 2], {1, 4}, {}], [[3, 2, 4, 5, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1}, {}], [[4, 1, 3, 5, 2], {1, 4}, {}], [[4, 2, 3, 5, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1}, {}], [[5, 1, 3, 4, 2], {1, 4}, {}], [[5, 2, 3, 4, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2080, 10888, 60027, 346470, 2084037, 13015686, 84145761, 561683258, 3862726447, 27315864554, 198303695666, 1475710973714, 11242307700827, 87575157415596] "" "Class ", 675, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {3}, {}], [[1, 3, 4, 2, 5], {3}, {}], [[1, 3, 5, 2, 4], {4}, {}], [[1, 3, 5, 4, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3}, {}], [[1, 4, 3, 5, 2], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1}, {}], [[2, 1, 4, 5, 3], {1}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3}, {}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {4}, {}], [[2, 3, 5, 4, 1], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3}, {}], [[2, 4, 3, 5, 1], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1}, {}], [[3, 1, 4, 5, 2], {1}, {}], [[3, 2, 4, 5, 1], {1}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3}, {}], [[3, 4, 2, 5, 1], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {}], [[3, 4, 5, 2, 1], {4}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1}, {}], [[4, 1, 3, 5, 2], {1}, {[0, 0, 1, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 4, 2], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 386, 1678, 7290, 31490, 135075, 575482, 2436985, 10265673, 43048763, 179827138, 748702990, 3108296537, 12872380989, 53193182050, 219395598552] "" "Class ", 676, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2532, 15617, 106607, 798305, 6508075, 57384779, 544186140, 5522898056, 59728159876, 685688935531, 8327956746156, 106683264001207, 1437529611800588, 20324985240891992] "" "Class ", 677, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 678, " is:" {{[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]} "Class ", 679, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 3, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 3, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 3, 4], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 3, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 3, 5, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 103, 518, 2861, 17095, 109327, 742440, 5321806, 40075109, 315839372, 2597089834, 22223418937, 197460408867, 1818303768056, 17323836243978, 170517168855064, 1731646972663090] "" "Class ", 680, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 503, 2901, 18493, 128581, 965586, 7770724, 66593820, 604547694, 5788068092, 58224507040, 613384213370, 6748064640656, 77331836812070, 921095509145838, 11380348764942244] "" "Class ", 681, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2694, 16694, 112846, 824206, 6455096, 53873556, 476643726, 4450852754, 43700071970, 449663208542, 4835182933672, 54194971717408, 631753349286450, 7643690289791254] "" "Class ", 682, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2705, 16799, 113809, 833110, 6539444, 54698372, 484995516, 4538513884, 44653841990, 460414303856, 4960633167622, 55708793664726, 650625055350856, 7886476216592946] "" "Class ", 683, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 2]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 684, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 685, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 686, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 687, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 2]}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 2]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 2]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 2]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 2]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, { [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}], [ [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 2]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 420, 2036, 10300, 53778, 287658, 1568334, 8683686, 48696704, 276015568, 1578751008, 9101044496, 52823187292, 308427262356, 1810410176580, 10676951738460] "" "Class ", 688, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 5, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 493, 2809, 17657, 120900, 893061, 7063421, 59452411, 529833085, 4978111298, 49130873120, 507726612474, 5478786535431, 61581842835417, 719427899313733, 8718454867896295] "" "Class ", 689, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2428, 14170, 89280, 602330, 4322954, 32830844, 262671216, 2205665682, 19375902218, 177566724134, 1693442102110, 16770380947302, 172122045247390, 1827656821652056] "" "Class ", 690, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [0, 1, 0]]} "Class ", 691, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2181, 12030, 71182, 448741, 2997674, 21124712, 156447457, 1213673841, 9834669852, 83034709705, 728856722470, 6638196514486, 62619948576947, 610847538821697] "" "Class ", 692, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 1]]} "Class ", 693, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2232, 12205, 70685, 430113, 2732971, 18046134, 123350475, 870004893, 6315043483, 47069008673, 359559476866, 2810416053212, 22444743553851, 182919057895545] "" "Class ", 694, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [0, 1, 1]]} "Class ", 695, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 2, 4], [1, 1, 1]]} "Class ", 696, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {3}, %1], [[1, 3, 5, 4, 2], {3, 4}, %1], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3}, %1], [[2, 3, 5, 4, 1], {3, 4}, %1], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 493, 2813, 17722, 121703, 902277, 7166659, 60608807, 542950618, 5129823568, 50926743827, 529530939036, 5750620631594, 65063308114309, 765236280061606, 9337565561953803] "" "Class ", 697, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2612, 16050, 107710, 781788, 6089496, 50577528, 445561453, 4144567358, 40550954611, 415935803076, 4459538229289, 49851297957672, 579689132224074, 6997771487022262] "" "Class ", 698, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 699, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 700, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2548, 15192, 97863, 675227, 4957343, 38526500, 315606721, 2715749321, 24474210325, 230410713797, 2261056580199, 23082662478421, 244718044265736, 2690072583445831] "" "Class ", 701, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 702, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 703, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 704, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 705, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 706, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 707, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 393, 1791, 8415, 40470, 198292, 986634, 4973257, 25348589, 130452875, 677046899, 3540113116, 18633157627, 98655097725, 525114137681, 2808424787327] "" "Class ", 708, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 709, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1839, 8908, 44646, 230171, 1215281, 6549146, 35925658, 200166611, 1130756422, 6466817843, 37394847767, 218408221877, 1287253794311, 7649846273933] "" "Class ", 710, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 711, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 380, 1678, 7584, 34875, 162560, 766124, 3644066, 17469863, 84324840, 409471090, 1998933556, 9804748548, 48298256084, 238840150970, 1185256302910] "" "Class ", 712, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 713, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 714, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 715, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 2, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 2, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 374, 1593, 6812, 29151, 124739, 533681, 2283044, 9766113, 41775068, 178692852, 764354624, 3269502578, 13985181673, 59821101977, 255882544027] "" "Class ", 716, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 717, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [ [1, 2, 4, 3], {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, 3, 2, 4], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 399, 1873, 9195, 46783, 245138, 1316640, 7222427, 40347679, 229021167, 1318373485, 7684756169, 45298305621, 269718954987, 1620709658427, 9819879943868] "" "Class ", 718, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 719, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 2, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 2, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 364, 1522, 6380, 26748, 112112, 469820, 1968668, 8248964, 34563872, 144825392, 606830152, 2542668584, 10653994208, 44641131544, 187050100128] "" "Class ", 720, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {3, 4, 5}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {3, 4, 5}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4, 5}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 502, 2882, 18264, 126068, 938946, 7489272, 63579870, 571570134, 5417744898, 53946694184, 562498509730, 6124554247480, 69462921014004, 818850289644242, 10013272987554916] "" "Class ", 721, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {3, 4, 5}, {[0, 0, 0, 0, 0, 1]}], [ [1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {3, 4, 5}, {[0, 0, 0, 0, 0, 1]}], [ [2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4, 5}, {[0, 0, 0, 0, 0, 1]}], [ [3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [ [4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2527, 15010, 96372, 663092, 4856241, 37646949, 307519441, 2636633932, 23649697214, 221287382150, 2154545711139, 21780269042451, 228152823839143, 2472175555865624] "" "Class ", 722, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 1, 0]]} "Class ", 723, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622] "" "Class ", 724, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {4}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {4}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2, 4}, {}], [[2, 5, 3, 4, 1], {2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2660, 16288, 108519, 779936, 6005267, 49256659, 428331858, 3932740163, 37988802961, 384850794579, 4077453981783, 45066860429156, 518463305506591, 6195642675421079] "" "Class ", 725, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2250, 12430, 73122, 454765, 2973971, 20364900, 145543062, 1082708058, 8365576807, 67012315975, 555667540893, 4763152744032, 42157951417892, 384866085706981] "" "Class ", 726, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [0, 1, 1]]} "Class ", 727, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 728, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "Class ", 729, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [ [3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2128, 11406, 64839, 388201, 2434382, 15918433, 108142142, 760915327, 5530802795, 41435547826, 319331263106, 2527247703739, 20508458178326, 170415807116212] "" "Class ", 730, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "Class ", 731, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 2]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 2], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 2]}], [[3, 1, 2], {1}, {[0, 0, 0, 2]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 404, 1949, 10002, 54148, 307349, 1820242, 11203946, 71441733, 470642550, 3195813851, 22323067412, 160121713523, 1177614956252, 8867905582187, 68292730537974] "" "Class ", 732, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "Class ", 733, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 734, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "Class ", 735, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {2}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 4, 2], {3, 4}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 5, 2], {2, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2}, {}], [[1, 5, 3, 4, 2], {2, 4}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 4, 1], {3, 4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {2, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {2, 4}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 3}, %1], [[3, 2, 4, 5, 1], {1, 3}, %1], [[3, 4, 1, 5, 2], {1, 2}, %1], [[3, 4, 2, 1, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2}, %1], [[3, 5, 2, 1, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[4, 5, 2, 1, 3], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1}, {}], [[5, 1, 3, 4, 2], {1, 4}, {}], [[5, 2, 3, 4, 1], {1, 4}, {}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 372, 1636, 7412, 34364, 162272, 777800, 3774552, 18509104, 91572096, 456530448, 2291277024, 11567413856, 58702288464, 299288512464, 1532268422432] "" "Class ", 736, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 502, 2882, 18264, 126068, 938946, 7489272, 63579870, 571570134, 5417744898, 53946694184, 562498509730, 6124554247480, 69462921014004, 818850289644242, 10013272987554916] "" "Class ", 737, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2601, 15857, 105283, 754277, 5788215, 47292357, 409339763, 3737402825, 35863892617, 360548676966, 3786838832038, 41449949383316, 471791783889456, 5573135192456863] "" "Class ", 738, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]} "Class ", 739, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2321, 13293, 82219, 544921, 3845615, 28747967, 226651233, 1877582984, 16290403577, 147616737052, 1393590616210, 13676530317121, 139252811925530, 1468422556788841] "" "Class ", 740, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "Class ", 741, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2127, 11378, 64420, 383184, 2380755, 15379449, 102909959, 711078605, 5060466247, 37009611940, 277627623421, 2132636421715, 16751273561232, 134369351462612] "" "Class ", 742, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]} "Class ", 743, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]} "Class ", 744, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {3}, %1], [[1, 3, 5, 4, 2], {3, 4}, %1], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3}, %1], [[2, 3, 5, 4, 1], {3, 4}, %1], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 502, 2894, 18418, 127840, 958151, 7694652, 65794492, 595902483, 5691677106, 57115964946, 600233585656, 6587188661968, 75303371420818, 894750295484463, 11028149877975410] "" "Class ", 745, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2694, 16694, 112846, 824206, 6455096, 53873556, 476643726, 4450852754, 43700071970, 449663208542, 4835182933672, 54194971717408, 631753349286450, 7643690289791254] "" "Class ", 746, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 747, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 748, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2526, 15004, 96417, 664864, 4888285, 38119687, 313917742, 2719883611, 24715636754, 234897312912, 2329222714251, 24045325861653, 257925778848485, 2869743339618779] "" "Class ", 749, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "Class ", 750, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 751, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 752, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 753, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 754, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 755, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 756, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 757, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 758, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 759, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 760, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]} "Class ", 761, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]} "Class ", 762, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 763, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 764, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "Class ", 765, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "Class ", 766, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 767, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 768, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2763, 17430, 120152, 895764, 7163632, 61050741, 551462695, 5255823074, 52649187209, 552494896438, 6056143852101, 69166027554599, 821185050893152, 10115059408156060] "" "Class ", 769, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, %1], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, %1], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, %1], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, %1], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, %1], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2528, 15336, 101446, 725071, 5557979, 45409644, 393388704, 3597769996, 34605600334, 348930773471, 3677613801241, 40413473057899, 461997652939027, 5483139819805956] "" "Class ", 770, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]} "Class ", 771, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]} "Class ", 772, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {4}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {4}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2, 4}, {}], [[2, 5, 3, 4, 1], {2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2504, 15148, 100212, 718006, 5527652, 45427414, 396357860, 3654615196, 35470067560, 361128413358, 3845403514912, 42712890237018, 493739365271352, 5927226509139340] "" "Class ", 773, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2184, 12096, 72104, 459440, 3111616, 22292592, 168263312, 1333377904, 11059335280, 95753379216, 863373139824, 8089902823120, 78625465178608, 791248858589264] "" "Class ", 774, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]} "Class ", 775, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]} "Class ", 776, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 777, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2195, 12095, 71197, 444343, 2922488, 20156942, 145208497, 1088887065, 8475304577, 68302940820, 568732037524, 4883680464196, 43175761755118, 392416375224309] "" "Class ", 778, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 779, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 780, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 781, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 782, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 783, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 784, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} "Class ", 785, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "Class ", 786, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} "Class ", 787, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} "Class ", 788, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2168, 11875, 69433, 429849, 2798780, 19063982, 135249552, 995756955, 7584660367, 59614957569, 482438728553, 4011974059179, 34227096974462, 299110991737943] "" "Class ", 789, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 401, 1917, 9737, 52094, 291916, 1704945, 10338909, 64890309, 420396231, 2804983173, 19237246825, 135380879992, 976165310371, 7202190207881, 54308368228799] "" "Class ", 790, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} "Class ", 791, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} "Class ", 792, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {3, 4}, %1], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, %1], [[1, 4, 2, 5, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3, 4}, %1], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, %1], [[2, 4, 1, 5, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 1, 5, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2616, 16050, 107262, 773519, 5973224, 49087120, 427091100, 3917413697, 37740795945, 380695132679, 4009545657441, 43984961745630, 501489994913243, 5930975520754786] "" "Class ", 793, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2195, 12095, 71197, 444343, 2922488, 20156942, 145208497, 1088887065, 8475304577, 68302940820, 568732037524, 4883680464196, 43175761755118, 392416375224309] "" "Class ", 794, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 795, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 796, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2225, 12609, 77494, 512655, 3626781, 27288698, 217395169, 1826591523, 16132299243, 149327729590, 1444935629325, 14581951220998, 153157961531641, 1671107896171084] "" "Class ", 797, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "Class ", 798, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 799, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 800, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "Class ", 801, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 802, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 803, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} "Class ", 804, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "Class ", 805, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 806, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {3, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {2, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1846, 9056, 46590, 250792, 1409970, 8265468, 50443786, 320019788, 2107396710, 14385165112, 101650730022, 742661974608, 5603308351978, 43610081811140] "" "Class ", 807, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 808, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]} "Class ", 809, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]} "Class ", 810, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]} "Class ", 811, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]} "Class ", 812, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]} "Class ", 813, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]} "Class ", 814, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2}, {}], [[1, 3, 5, 4, 2], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2}, {}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2}, {}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1}, {}], [[2, 1, 4, 5, 3], {1, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3}, {}], [[2, 3, 5, 4, 1], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1}, {}], [[3, 1, 4, 5, 2], {1, 3}, {}], [[3, 2, 4, 5, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1}, {}], [[4, 1, 3, 5, 2], {1, 3}, {}], [[4, 2, 3, 5, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1}, {}], [[5, 1, 3, 4, 2], {1, 3}, {}], [[5, 2, 3, 4, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 390, 1746, 7988, 37163, 175427, 839411, 4069685, 19987466, 99428044, 500917235, 2555515283, 13200486685, 69029764152, 365382101255, 1957250514297] "" "Class ", 815, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2}, {}], [[1, 3, 5, 4, 2], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2}, {}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 4, 2], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1}, {}], [[2, 1, 4, 5, 3], {1, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {3}, {}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {4}, {}], [[2, 3, 5, 4, 1], {1, 5}, %1], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {}], [[2, 5, 3, 4, 1], {1, 5}, %1], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1}, {}], [[3, 1, 4, 5, 2], {1, 3}, {}], [[3, 2, 4, 5, 1], {1}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {}], [[3, 4, 5, 2, 1], {4}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1}, {}], [[4, 1, 3, 5, 2], {1, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 4, 2], {2, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 5}, %1]} %1 := {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 358, 1437, 5650, 21772, 82446, 307695, 1134634, 4142703, 15001490, 53949985, 192895723, 686286826, 2431348482, 8582195720, 30197196113] "" "Class ", 816, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2836, 17998, 124606, 931820, 7468606, 63755512, 576618866, 5500881236, 55145210544, 579025771201, 6349869252427, 72546756589732, 861567610731846, 10614837157637645] "" "Class ", 817, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2442, 14452, 93154, 648451, 4840287, 38512334, 324996954, 2896293348, 27156676090, 267038795648, 2745982325336, 29454333011234, 328813144463625, 3812572723414315] "" "Class ", 818, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 819, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 820, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, %1], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, %1], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 3, 2, 5], {1, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 1, 5], {1, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 3, 2, 4], {1, 4}, %1], [[5, 1, 4, 2, 3], {2, 3}, {}], [[5, 1, 4, 3, 2], {4}, {}], [[5, 2, 3, 1, 4], {1, 4}, %1], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 2, 4, 3, 1], {4}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {4}, {}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2579, 15666, 103738, 742294, 5698665, 46660686, 405438983, 3722362700, 35974784270, 364780361892, 3869471038493, 42828326410580, 493470007168653, 5906535498076700] "" "Class ", 821, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 4, 5, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 4, 5, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2133, 11512, 66332, 405762, 2623064, 17851077, 127468493, 952299010, 7424602910, 60272849038, 508440074044, 4448714757285, 40307608557993, 377608585783432] "" "Class ", 822, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 823, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 824, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 825, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2155, 11949, 71999, 468252, 3266955, 24321257, 192282581, 1607618208, 14161708972, 131016945275, 1269305129984, 12844403901905, 135446948998603, 1485350383106707] "" "Class ", 826, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 827, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 828, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 829, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 1, 5], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 378, 1650, 7328, 32926, 149136, 679299, 3106318, 14243972, 65443158, 301092342, 1386646562, 6390603637, 29467471794, 135927784974, 627183516100] "" "Class ", 830, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 831, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 832, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 833, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2103, 11215, 63738, 383829, 2436272, 16224462, 112913652, 818414488, 6159822431, 48019245759, 386843716496, 3214136957481, 27493705788907, 241743676924432] "" "Class ", 834, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 835, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 836, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2170, 11841, 68864, 423672, 2740959, 18554678, 130878862, 958516875, 7266253595, 56865351207, 458362278813, 3797692691467, 32286056166885, 281203558660327] "" "Class ", 837, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 395, 1819, 8709, 43138, 220526, 1161309, 6291463, 35020752, 200065817, 1171729082, 7028102148, 43130348195, 270556974371, 1733345223471, 11331922253037] "" "Class ", 838, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 839, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 840, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]} "Class ", 841, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [ [1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2178, 12142, 73519, 480277, 3364536, 25140890, 199441021, 1672728404, 14778396431, 137094218519, 1331549700411, 13506178023934, 142741158737138, 1568594325403514] "" "Class ", 842, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]} "Class ", 843, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 844, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2189, 12201, 73603, 477812, 3320280, 24575637, 192902125, 1599521664, 13962876417, 127928489272, 1226835619434, 12284946511517, 128166108904261, 1390340997269911] "" "Class ", 845, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [ [4, 1, 2, 3], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 3, 2, 5], {1, 4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [ [5, 1, 3, 2, 4], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {[1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1846, 9047, 46394, 248174, 1381739, 7992596, 47955156, 297992918, 1915037930, 12710648855, 87022911369, 613856325161, 4456466042367, 33262745913461] "" "Class ", 846, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]} "Class ", 847, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 848, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 849, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [1, 3, 5, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 2, 3}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 421, 2073, 10916, 61124, 362162, 2259298, 14777344, 100951456, 718018613, 5301788393, 40542688100, 320368513630, 2610973456836, 21908605988520, 188981220913614] "" "Class ", 850, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 851, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3}, %1], [[1, 4, 2, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, %1], [[2, 1, 4, 5, 3], {1, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3}, %1], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, %1], [[3, 1, 4, 5, 2], {1, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 5, 1], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 3, 5, 2], {1, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 5, 1], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 4, 2], {1, 4}, %1], [[5, 2, 3, 4, 1], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 387, 1709, 7682, 35022, 161593, 753389, 3544594, 16810850, 80295382, 385951456, 1865651100, 9064417504, 44243703313, 216862177265, 1067036101280] "" "Class ", 852, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 853, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 3, 5, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 3, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [5, 1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 370, 1522, 6057, 22973, 82141, 274760, 856489, 2487897, 6752855, 17203136, 41344530, 94228533, 204671556, 425623698, 850890704] "" "Class ", 854, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 855, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3}, %2], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 4}, %2], [[1, 4, 2, 5, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, %2], [[2, 1, 4, 5, 3], {1}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3}, %2], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 4}, %2], [[2, 4, 1, 5, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {3}, %1], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {4}, %1], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, %2], [[3, 1, 4, 5, 2], {1}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 5, 1], {1}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [ [4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 3, 5, 2], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1}, %1]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 351, 1331, 4689, 15217, 45454, 125396, 321294, 769606, 1734871, 3703689, 7531205, 14661591, 27450082, 49621234, 86906318] "" "Class ", 856, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[1, 0, 0, 0, 0]}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[1, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 5, 4, 2], {3}, %2], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 5, 4, 1], {3}, %1], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {4}, %2], [[5, 1, 3, 4, 2], {1}, %2], [[5, 1, 4, 2, 3], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 1, 4], {4}, %1], [[5, 2, 3, 4, 1], {1}, %1], [[5, 2, 4, 1, 3], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 379, 1594, 6556, 26074, 99576, 364291, 1278541, 4320807, 14128868, 44904291, 139270323, 422951303, 1261259992, 3701884427, 10714896492] "" "Class ", 857, " is:" {{[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]} "Class ", 858, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 491, 2782, 17355, 117668, 858781, 6696157, 55443476, 485054802, 4465117634, 43095711555, 434775319901, 4572637644197, 50017286957177, 567832132827270, 6678165429960074] "" "Class ", 859, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2577, 15622, 103051, 732936, 5578977, 45171990, 387079192, 3495237142, 33135900270, 328761338650, 3404176630265, 36696637813076, 410938144076555, 4771075755829682] "" "Class ", 860, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 861, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2253, 12489, 73905, 463641, 3067253, 21309136, 154941030, 1175814468, 9290869447, 76283885208, 649665221137, 5729711345123, 52255939949136, 492183451384767] "" "Class ", 862, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2411, 13963, 87042, 579259, 4088943, 30457287, 238374743, 1953283669, 16706473009, 148757363759, 1375787882351, 13189453993725, 130835235093995, 1340746108292891] "" "Class ", 863, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2146, 11624, 67146, 411142, 2656052, 18035178, 128318314, 954086192, 7396278762, 59659032142, 499778527628, 4341025729290, 39035256389026, 362878164902216] "" "Class ", 864, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2232, 12205, 70685, 430113, 2732971, 18046134, 123350475, 870004893, 6315043483, 47069008673, 359559476866, 2810416053212, 22444743553851, 182919057895545] "" "Class ", 865, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 408, 1938, 9615, 49354, 260359, 1404687, 7722264, 43135238, 244268319, 1399801325, 8105718991, 47371292042, 279123783658, 1656778588642, 9899228458769] "" "Class ", 866, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2511, 14814, 94224, 640544, 4623015, 35232159, 282270209, 2368591365, 20751308498, 189300733507, 1793842203203, 17621328395632, 179107898763397, 1880600989964981] "" "Class ", 867, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]} "Class ", 868, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 493, 2809, 17644, 120541, 886841, 6972414, 58217625, 513641542, 4768304343, 46409629424, 472120617821, 5006486305848, 55210797393839, 631855774614925, 7490380379752677] "" "Class ", 869, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2577, 15622, 103051, 732936, 5578977, 45171990, 387079192, 3495237142, 33135900270, 328761338650, 3404176630265, 36696637813076, 410938144076555, 4771075755829682] "" "Class ", 870, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 871, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 872, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2581, 15590, 102193, 720426, 5423381, 43348119, 366112600, 3254256966, 30337698743, 295738012734, 3006674651729, 31806332160940, 349374642791060, 3977541917759969] "" "Class ", 873, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 3}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2285, 12856, 77631, 499550, 3406399, 24501854, 185196468, 1466177110, 12123823416, 104453217908, 935587202671, 8695177235306, 83702799511281, 833251637996702] "" "Class ", 874, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 875, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 876, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 491, 2778, 17284, 116759, 848292, 6579643, 54159489, 470800041, 4304357701, 41245411433, 412983342397, 4309633783080, 46762363974861, 526514550823092, 6140242335409203] "" "Class ", 877, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [ [1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 451, 2375, 13517, 82219, 530122, 3600242, 25625004, 190372814, 1471276315, 11795144687, 97855301953, 838364471865, 7403879590068, 67292762679396, 628553373970988] "" "Class ", 878, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 879, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 880, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2492, 14898, 96740, 676334, 5054712, 40148126, 337247152, 2983672994, 27703433136, 269127649450, 2728059162792, 28786214210198, 315521276267616, 3585582242680438] "" "Class ", 881, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 412, 2002, 10306, 55709, 314146, 1838880, 11130244, 69443396, 445473992, 2931927554, 19762407890, 136210309369, 958694809278, 6882401216326, 50342758287742] "" "Class ", 882, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2165, 11859, 69597, 434794, 2876584, 20068382, 147102044, 1129391080, 9057511918, 75695407892, 657803437814, 5932706331710, 55434949710352, 535798023308036] "" "Class ", 883, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 884, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[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, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 5, 4, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2551, 15221, 98041, 675495, 4942465, 38186341, 310076558, 2635891819, 23380122765, 215769297776, 2066732309734, 20501693742257, 210219955685135, 2224309394628429] "" "Class ", 885, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 5, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [ [1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2141, 11529, 65902, 397098, 2508534, 16541078, 113441070, 806750068, 5934297612, 45052450361, 352346487861, 2834068701373, 23410500306299, 198340840318963] "" "Class ", 886, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 887, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 888, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2317, 13168, 80333, 521571, 3580793, 25857819, 195552235, 1543189011, 12668176280, 107893707121, 951173177239, 8662101591546, 81340443301515, 786345013574944] "" "Class ", 889, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 402, 1922, 9714, 51478, 284254, 1627878, 9633270, 58732394, 368028578, 2365402962, 15566886898, 104744041478, 719662927598, 5043246470902, 36011158760022] "" "Class ", 890, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 891, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 892, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2126, 11367, 64379, 383701, 2394425, 15582153, 105400879, 739017066, 5358407866, 40096210374, 309088847824, 2450718396124, 19958478845001, 166741444511806] "" "Class ", 893, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, %1], [[1, 4, 2, 3], {2, 3}, %1], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 3}, %1], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {1, 3}, %1], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 401, 1904, 9512, 49566, 267715, 1491906, 8548197, 50222556, 301917529, 1853956171, 11612501233, 74108058336, 481390381951, 3180267637079, 21352845809091] "" "Class ", 894, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 503, 2903, 18449, 127458, 947720, 7526905, 63461198, 565166475, 5294166451, 51978680491, 533247273848, 5700984836904, 63368202653929, 730787629846144, 8727779474085650] "" "Class ", 895, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 479, 2675, 16441, 109866, 790740, 6084188, 49744443, 430018987, 3913852815, 37371082058, 373193377116, 3887075756764, 42127578436781, 474071505341603, 5528809533625671] "" "Class ", 896, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 897, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 898, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2520, 14997, 96777, 671577, 4977859, 39191722, 326225691, 2859441774, 26302003442, 253126469283, 2542029568157, 26576672815836, 288661418402443, 3251082041240479] "" "Class ", 899, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2238, 12345, 72759, 455491, 3014851, 21018376, 153842490, 1178879195, 9433772797, 78657738903, 681940480200, 6136053125898, 57204204476503, 551675297881865] "" "Class ", 900, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 901, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 902, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 429, 2205, 12358, 74837, 486447, 3376077, 24901540, 194403135, 1600609778, 13854028172, 125693684131, 1192225202470, 11794474237178, 121432907129280, 1298607309176079] "" "Class ", 903, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 904, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 2, 5, 4, 3], {2}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 3, 5, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2517, 14942, 96034, 662415, 4869705, 37942123, 311881547, 2694243139, 24379797686, 230426525351, 2269129827765, 23230246235296, 246753062187088, 2714688705027102] "" "Class ", 905, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2150, 11604, 66488, 401746, 2546335, 16858417, 116185765, 831135674, 6156121813, 47112922046, 371851115399, 3021961280475, 25250674246809, 216651082151598] "" "Class ", 906, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 907, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 908, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2082, 10940, 60795, 355245, 2172635, 13850081, 91720641, 629119648, 4458334329, 32570318026, 244827967287, 1890391518113, 14971031290594, 121444706197907] "" "Class ", 909, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1826, 8735, 43078, 218310, 1134791, 6042982, 32939388, 183651782, 1046656310, 6093356451, 36212908510, 219548758135, 1356951510973, 8544194332518] "" "Class ", 910, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 911, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 912, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2202, 12183, 72047, 451743, 2984263, 20667334, 149440578, 1124420023, 8778761865, 70946554516, 592262222708, 5097861768142, 45170423708198, 411425375360074] "" "Class ", 913, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 914, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 5, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2565, 15441, 100804, 707290, 5295943, 42077013, 353062110, 3116268313, 28835178661, 278893442494, 2812318203444, 29499427342603, 321222372518937, 3624526968797048] "" "Class ", 915, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2133, 11411, 64618, 384938, 2400537, 15611993, 105555023, 740004985, 5367272173, 40197050948, 310325390095, 2465856467506, 20140002984874, 168874624941140] "" "Class ", 916, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 917, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 918, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2218, 12502, 76276, 499823, 3497352, 26003607, 204562102, 1696260196, 14778001364, 134874196459, 1286172621538, 12785275208249, 132203465666840, 1419267381934368] "" "Class ", 919, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 383, 1717, 7943, 37775, 184486, 925217, 4765918, 25221180, 137134786, 766106662, 4396791881, 25917065821, 156853607302, 974276154953, 6207861551213] "" "Class ", 920, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 921, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 922, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 432, 2255, 12906, 80151, 535858, 3830652, 29115956, 234194964, 1985430736, 17678295810, 164818749719, 1604661788030, 16275424208001, 171602985254585, 1877269508724120] "" "Class ", 923, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [2, 3, 5, 4, 1], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 399, 1897, 9610, 51599, 292347, 1741363, 10870338, 70919621, 482399849, 3413737930, 25084082062, 191054089844, 1505981221119, 12267695733250, 103136879768764] "" "Class ", 924, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2573, 15584, 102622, 728005, 5521587, 44507211, 379360257, 3404881458, 32064173388, 315833651558, 3245188457752, 34699839124890, 385300651636917, 4434377145188824] "" "Class ", 925, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2162, 11937, 71294, 458088, 3148973, 23042070, 178703510, 1463350260, 12608606854, 113958266382, 1077424229085, 10629493690052, 109181528865005, 1165237986323186] "" "Class ", 926, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, %1], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, %1], [[1, 3, 5, 4, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 3, 5, 4, 1], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, %1], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, %1], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [ [4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2116, 11406, 65819, 404192, 2628363, 18023073, 129854332, 979965973, 7725056001, 63456328885, 541991072191, 4804088980605, 44113524315188, 418971967047272] "" "Class ", 927, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 2, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 5, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {3, 5}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 391, 1787, 8561, 42916, 224697, 1226279, 6962027, 41041828, 250793822, 1586074231, 10366174361, 69922980117, 486168703593, 3480301923345, 25623719781769] "" "Class ", 928, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2082, 10940, 60795, 355245, 2172635, 13850081, 91720641, 629119648, 4458334329, 32570318026, 244827967287, 1890391518113, 14971031290594, 121444706197907] "" "Class ", 929, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 373, 1574, 6580, 27028, 108839, 430176, 1673158, 6422789, 24398897, 91930221, 344176189, 1282223555, 4758784052, 17609937695, 65019698612] "" "Class ", 930, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [ [2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 5, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 388, 1724, 7807, 35875, 167066, 788361, 3771130, 18294975, 90048811, 449801225, 2280366732, 11733185684, 61262117273, 324514640944, 1743488112137] "" "Class ", 931, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [ [2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 2, 5, 3], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 3, 5, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [ [4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 354, 1390, 5269, 19264, 68191, 235070, 794025, 2642676, 8705298, 28480236, 92770038, 301397453, 977832501, 3170570735, 10280036041] "" "Class ", 932, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [ [1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2191, 12234, 73961, 481112, 3348386, 24803372, 194662665, 1612199464, 14040833369, 128189501573, 1223477359454, 12177297058731, 126111631752366, 1356255573616474] "" "Class ", 933, " is:" {{[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 934, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 469, 2482, 13960, 82349, 504828, 3194759, 20765507, 138085776, 936489543, 6461176120, 45256388216, 321266564830, 2308053336011, 16760746522369, 122901529451504] "" "Class ", 935, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 447, 2301, 12581, 72134, 429782, 2643315, 16697540, 107908950, 711235696, 4769032950, 32464909416, 223987343854, 1563996272378, 11038837462369, 78674737265262] "" "Class ", 936, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 937, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {2}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {5}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2072, 10716, 57736, 321528, 1840092, 10774846, 64337350, 390690822, 2407606470, 15029878486, 94909579612, 605506719314, 3898822568410, 25314556836800] "" "Class ", 938, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 435, 2195, 11749, 65931, 384590, 2317104, 14347926, 90958032, 588502397, 3876227241, 25936747035, 175998488201, 1209345467169, 8404193933269, 59003740864709] "" "Class ", 939, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1955, 9804, 51106, 275081, 1521251, 8610223, 49724445, 292274357, 1744984501, 10564161632, 64758903493, 401472390111, 2514485004042, 15895934702590] "" "Class ", 940, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 941, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 3, 1, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 2]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 942, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2210, 11903, 67287, 395654, 2403744, 15011028, 95969158, 626121474, 4157810085, 28043123779, 191768623633, 1327624762094, 9293414293443, 65707083544575] "" "Class ", 943, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {}], [[3, 5, 1, 4, 2], {1, 2}, {}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 1987, 10134, 53940, 297264, 1686157, 9799489, 58144839, 351225723, 2154907033, 13403466124, 84386110506, 537055305588, 3451261961091, 22373564473595] "" "Class ", 944, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 5, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 5, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 460, 2419, 13544, 79637, 487025, 3076230, 19963604, 132573461, 898025814, 6189063512, 43307035076, 307142045510, 2204648342116, 15996582725282, 117205827359726] "" "Class ", 945, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2227, 12085, 68912, 408949, 2507712, 15804933, 101958064, 671048962, 4494279454, 30564557761, 210701362160, 1470182867367, 10370323663062, 73870560617048] "" "Class ", 946, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 947, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 948, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 5, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2236, 12141, 69216, 410485, 2515020, 15837091, 102080480, 671354337, 4493460761, 30543045878, 210467595454, 1468121297328, 10353865327613, 73747231558695] "" "Class ", 949, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1971, 9969, 52520, 286096, 1602550, 9191305, 53797023, 320475640, 1938854690, 11891393143, 73826145459, 463374455992, 2937204664508, 18785301198693] "" "Class ", 950, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 951, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 952, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 953, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 954, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 393, 1791, 8415, 40470, 198292, 986634, 4973257, 25348589, 130452875, 677046899, 3540113116, 18633157627, 98655097725, 525114137681, 2808424787327] "" "Class ", 955, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2221, 11992, 67951, 400491, 2438821, 15266309, 97839977, 639943061, 4260762182, 28815975935, 197612385155, 1372103566168, 9633991587761, 68329114970574] "" "Class ", 956, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1839, 8908, 44646, 230171, 1215281, 6549146, 35925658, 200166611, 1130756422, 6466817843, 37394847767, 218408221877, 1287253794311, 7649846273933] "" "Class ", 957, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 958, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 959, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 393, 1807, 8648, 42783, 217558, 1132349, 6011811, 32468546, 177986353, 988515107, 5553856659, 31526092262, 180611347891, 1043335304888, 6072501987687] "" "Class ", 960, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 961, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[1, 3, 2], {2}, {[0, 0, 2, 0], [0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 2, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 87, 352, 1434, 5856, 23937, 97884, 400338, 1637470, 6697823, 27396816, 112064806, 458394724, 1875039929, 7669758220, 31372775038, 128328833274] "" "Class ", 962, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 963, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [ [1, 2, 4, 3], {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, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 371, 1623, 7299, 33549, 156973, 745460, 3585257, 17432765, 85579152, 423684438, 2113445547, 10614015146, 53632183071, 272512318031, 1391721796674] "" "Class ", 964, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 965, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[1, 3, 2], {2}, {[0, 0, 2, 0], [0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 2, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 87382, 349526, 1398102, 5592406, 22369622, 89478486, 357913942, 1431655766, 5726623062, 22906492246, 91625968982] "" "Class ", 966, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} "Class ", 967, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 968, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 5, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 5, 4, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 469, 2487, 14007, 82716, 507522, 3214288, 20907195, 139120068, 944098292, 6517614984, 45678490289, 324448554797, 2332221077780, 16945598469502, 124324696121025] "" "Class ", 969, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 447, 2301, 12581, 72134, 429782, 2643315, 16697540, 107908950, 711235696, 4769032950, 32464909416, 223987343854, 1563996272378, 11038837462369, 78674737265262] "" "Class ", 970, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 971, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 972, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 434, 2185, 11668, 65309, 379829, 2280397, 14062890, 88733716, 571091307, 3739681482, 24864536708, 167570836826, 1143044997429, 7882144751099, 54889294335309] "" "Class ", 973, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [ [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 408, 1940, 9656, 49884, 265898, 1455922, 8160697, 46694143, 272099737, 1611629501, 9685874228, 58981505744, 363452675263, 2263902308760, 14240604225414] "" "Class ", 974, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 975, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 976, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 977, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [ [3, 4, 2, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 87, 352, 1431, 5812, 23545, 95117, 383272, 1541023, 6184908, 24787516, 99229270, 396882780, 1586310655, 6337057501, 25305526158, 101021557814] "" "Class ", 978, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 979, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]} "Class ", 980, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [ [1, 2, 4, 3], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 398, 1857, 9028, 45327, 233632, 1230883, 6606559, 36031638, 199269955, 1115612079, 6313770875, 36079301498, 207964497326, 1208129850146, 7068295990657] "" "Class ", 981, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 982, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 983, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 391, 1769, 8275, 39880, 197338, 999498, 5166688, 27191170, 145382220, 788298840, 4328248775, 24033606734, 134813758984, 763215115089, 4357129111243] "" "Class ", 984, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 367, 1560, 6711, 29165, 128019, 567692, 2543393, 11511356, 52616921, 242789604, 1130391287, 5307569419, 25119028331, 119764553944, 574990667817] "" "Class ", 985, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 986, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 987, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 988, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "Class ", 989, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "Class ", 990, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 991, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 992, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1848, 9066, 46360, 245300, 1335500, 7449234, 42424456, 246020588, 1449501354, 8660991983, 52403035908, 320645306477, 1981961027948, 12363921068244] "" "Class ", 993, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [ [4, 1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3, 4}, %1], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3, 4}, %1], [[2, 5, 4, 1, 3], {1, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 1, 2], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 2, 3, 1, 5], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[5, 2, 3, 1, 4], {1, 2, 3, 4}, %1], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 87, 350, 1400, 5517, 21348, 81074, 302447, 1109885, 4012875, 14317103, 50477408, 176090785, 608503704, 2084993891, 7089808379, 23942954256] "" "Class ", 994, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 995, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 996, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 365, 1539, 6548, 28034, 120631, 521399, 2262806, 9857186, 43088973, 188963005, 831158463, 3666017767, 16211533878, 71861270688, 319253827311] "" "Class ", 997, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]} "Class ", 998, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]} "Class ", 999, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]} "Class ", 1000, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 2, 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]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [ [2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [2, 5, 1, 3, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 4}, {[0, 0, 2, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 358, 1443, 5718, 22253, 85148, 320832, 1192238, 4375526, 15878466, 57037673, 203000654, 716430483, 2509043720, 8725298030, 30146655078] "" "Class ", 1001, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]} "Class ", 1002, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]} "Class ", 1003, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3}, %1], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3}, %2], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3}, %2], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, %1], [[2, 1, 4, 5, 3], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3}, %1], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 5, 3, 4, 1], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, %1], [[3, 1, 4, 5, 2], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 5, 1], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, %2], [[4, 1, 3, 5, 2], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 5, 1], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3}, %2], [[5, 1, 3, 4, 2], {1, 3}, %1], [ [5, 2, 3, 4, 1], {1, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 353, 1364, 5004, 17435, 58092, 186676, 583195, 1783291, 5366022, 15955485, 47028176, 137723897, 401426653, 1165973111, 3377893590] "" "Class ", 1004, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3}, %1], [[1, 4, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3}, %1], [[2, 1, 4, 5, 3], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3}, %1], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 4}, %1], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 5, 1], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3}, %1], [[3, 1, 4, 5, 2], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 5, 1], {1}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [ [4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 3, 5, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [ [4, 2, 3, 5, 1], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 321, 1085, 3266, 8797, 21478, 48206, 100728, 198046, 369617, 659505, 1131656, 1876481, 3018946, 4728382, 7230242] "" "Class ", 1005, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 1, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 398, 1871, 9249, 47673, 254408, 1397390, 7862663, 45150714, 263845046, 1565477449, 9414103425, 57293628682, 352447508868, 2189222487982, 13718407227059] "" "Class ", 1006, " is:" {{[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 1007, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 555, 3534, 25730, 210688, 1915941, 19166822, 209167950, 2472790829, 31482426779, 429448585354, 6248587853622, 96601065245554, 1581267812707760, 27321842165630452, 496925125639322326] "" "Class ", 1008, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3094, 21044, 159618, 1335711, 12224425, 121462164, 1302086835, 14979521941, 184074392017, 2406324891719, 33343799377788, 488182955862266, 7530243579604926, 122059134990479181] "" "Class ", 1009, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1010, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1011, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3053, 20471, 152362, 1245665, 11094692, 106903767, 1107819708, 12284238016, 145118996819, 1819393002777, 24125640256241, 337339263479915, 4960353206819621, 76516294948472951] "" "Class ", 1012, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2680, 16442, 109493, 784101, 5994355, 48634329, 416743177, 3756245864, 35489182724, 350426366428, 3606812722097, 38608062980459, 428916270860660, 4936422983035828] "" "Class ", 1013, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1014, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1015, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 540, 3388, 24248, 195048, 1742860, 17127880, 183617280, 2132433940, 26669752928, 357375269160, 5108084756320, 77574769941760, 1247401873186560, 21172559509803520, 378282904982091200] "" "Class ", 1016, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3068, 20873, 158951, 1340391, 12404293, 125005852, 1362830756, 15982235660, 200620521905, 2683993410039, 38124488181544, 573028830332350, 9086323419918599, 151586673816986103] "" "Class ", 1017, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 1018, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 1019, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3}, {}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2923, 19210, 139863, 1116973, 9706879, 91173274, 920284345, 9933627109, 114173030457, 1392055982170, 17944919653279, 243852952745977, 3483842196002323, 52202044881041902] "" "Class ", 1020, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2656, 16213, 107438, 766004, 5834251, 47196241, 403564132, 3632772331, 34306277357, 338850074178, 3491324087927, 37437229679201, 416908472504244, 4812674688078162] "" "Class ", 1021, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 1022, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 1023, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 556, 3550, 25923, 212960, 1943217, 19506469, 213611655, 2534107378, 32375275725, 443164501881, 6470602066227, 100381490487147, 1648868927774609, 28589048157501712, 521782697091746412] "" "Class ", 1024, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3094, 21044, 159618, 1335711, 12224425, 121462164, 1302086835, 14979521941, 184074392017, 2406324891719, 33343799377788, 488182955862266, 7530243579604926, 122059134990479181] "" "Class ", 1025, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 1026, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 1027, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3074, 20774, 156265, 1294579, 11712445, 114896782, 1214692633, 13767554019, 166535525193, 2141343769320, 29165230876044, 419450825574743, 6352014599275973, 101031127834456302] "" "Class ", 1028, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2500, 14631, 91954, 615424, 4357970, 32484903, 253844908, 2072320828, 17623569457, 155742520219, 1427144689271, 13535113824562, 132637939599729, 1341038776606735] "" "Class ", 1029, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 1030, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 1031, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 552, 3514, 25552, 208959, 1898932, 18981130, 206983062, 2445163135, 31107582576, 424021802910, 6165078296956, 95239714398489, 1557833683405776, 26897084750393974, 488838858664973126] "" "Class ", 1032, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 508, 3016, 20181, 150501, 1238590, 11156322, 109193522, 1154125930, 13101971134, 158997878326, 2054051250009, 28144941517011, 407698261408191, 6225241453305309, 99932935194161898] "" "Class ", 1033, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 1034, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 1035, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 533, 3276, 22754, 176400, 1508905, 14119130, 143433016, 1572136136, 18491585875, 232317793504, 3104805097092, 43981005945074, 658232398394641, 10378379944857470, 171945895681581744] "" "Class ", 1036, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 490, 2775, 17307, 117414, 858109, 6704984, 55669340, 488648513, 4515345655, 43764835898, 443549513262, 4687683942514, 51538661683224, 588224911846667, 6956078577022724] "" "Class ", 1037, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 1038, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 1039, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 509, 3018, 20124, 148940, 1211270, 10734633, 102947075, 1062071784, 11727406785, 137988562126, 1723449859956, 22771156034067, 317308101253152, 4650533160315976, 71512556630751394] "" "Class ", 1040, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {2}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {2, 3, 4}, {}], [[4, 2, 3, 5, 1], {2, 3, 4}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3057, 20530, 153058, 1253586, 11183781, 107917652, 1119623026, 12425219536, 146846869215, 1841067657914, 24402439099022, 340905477367574, 5005983733733449, 77078781496259512] "" "Class ", 1041, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {2}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 5, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2654, 16191, 107227, 764137, 5818775, 47076451, 402744082, 3628832932, 34318081764, 339624312800, 3507956829072, 37729360056849, 421669967273256, 4887912979572979] "" "Class ", 1042, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3078, 20964, 159760, 1347866, 12477362, 125768360, 1371339518, 16083673098, 201909343806, 2701396186164, 38373487962452, 576793333001200, 9146301327235326, 152591246547025020] "" "Class ", 1043, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 462, 2475, 14398, 89988, 599503, 4230956, 31475568, 245826060, 2008717400, 17123119202, 151889610113, 1398940391423, 13352176526581, 131835925117640, 1344521505373108] "" "Class ", 1044, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2687, 16584, 111506, 809268, 6293064, 52116487, 457333769, 4234203305, 41208610887, 420232584211, 4477706516566, 49728512226528, 574350314318354, 6885046186102775] "" "Class ", 1045, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 444, 2255, 12112, 67998, 395735, 2372871, 14590558, 91666440, 586712355, 3816745765, 25186870800, 168333215186, 1137871448886, 7770454973334, 53555423350804] "" "Class ", 1046, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3414, 24550, 198532, 1783802, 17629694, 190079142, 2220184596, 27927356678, 376386845670, 5410880990854, 82647658559140, 1336646994646962, 22818337281497918, 410041352131279094] "" "Class ", 1047, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 495, 2869, 18624, 133891, 1056698, 9087063, 84601113, 847955530, 9104762361, 104271580292, 1268767955176, 16346265038865, 222297564531874, 3182194293742849, 47830805246713509] "" "Class ", 1048, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {2, 4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {2}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {2, 3, 4}, {}], [[4, 2, 3, 5, 1], {2, 3, 4}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3167, 21620, 164141, 1371131, 12492603, 123253338, 1308758813, 14878693639, 180280374267, 2318954088280, 31555901588853, 452863642307547, 6835156034083883, 108228038363573070] "" "Class ", 1049, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {2}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 489, 2752, 17026, 114395, 827219, 6392429, 52485200, 455667866, 4166207358, 39976573642, 401358575822, 4205067782643, 45868063447427, 519802390640446, 6108615070164611] "" "Class ", 1050, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3040, 20436, 153056, 1264448, 11426458, 112145566, 1188073256, 13513832696, 164272027426, 2125285580904, 29158301898976, 422856332966192, 6463224865759038, 103847515324427030] "" "Class ", 1051, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 1052, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2804, 17658, 121334, 900874, 7171560, 60825134, 546749909, 5185649459, 51698478911, 539990548423, 5892260486803, 66998723819185, 792071246475925, 9716339134252969] "" "Class ", 1053, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 1054, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3406, 24422, 196805, 1761350, 17336372, 186127798, 2164750282, 27113108494, 363839033409, 5207940666250, 79204654879126, 1275435509472710, 21679396442301324, 387893197940671918] "" "Class ", 1055, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2952, 19543, 143514, 1156920, 10154697, 96374458, 983187204, 10727827066, 124649776016, 1536441262850, 20022556261395, 275040581877513, 3971718632568791, 60146544228837727] "" "Class ", 1056, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1057, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1058, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2952, 19540, 143579, 1159185, 10198031, 97095388, 994586822, 10905648785, 127443492169, 1581123073901, 20754536888042, 287368297200414, 4185604874304519, 63973825751776053] "" "Class ", 1059, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 1, 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, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2408, 13891, 85962, 565883, 3937482, 28813259, 220840678, 1766948413, 14716646204, 127290811525, 1141018761017, 10580663229191, 101336366811039, 1000996925348058] "" "Class ", 1060, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1061, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1062, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 540, 3403, 24488, 198288, 1783918, 17654956, 190609848, 2229404584, 28081272032, 378972914760, 5455420114672, 83440556575552, 1351293697714752, 23099544097433452, 415655429905054064] "" "Class ", 1063, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 524, 3207, 22256, 172858, 1485179, 13988328, 143308610, 1586642041, 18877946639, 240216275950, 3255256316097, 46804249432510, 711647757251186, 11408787458124773, 192332399896097976] "" "Class ", 1064, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1065, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1066, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2884, 18799, 135733, 1075459, 9277318, 86545863, 868116611, 9316526103, 106510317545, 1292220112183, 16581452509758, 224359123079065, 3192477638348599, 47655973641407301] "" "Class ", 1067, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2656, 16213, 107438, 766004, 5834251, 47196241, 403564132, 3632772331, 34306277357, 338850074178, 3491324087927, 37437229679201, 416908472504244, 4812674688078162] "" "Class ", 1068, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1069, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1070, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 545, 3456, 25035, 203949, 1846066, 18381359, 199658792, 2349421177, 29772690943, 404239329523, 5854473714423, 90087807504086, 1467802953158405, 25243559963919431, 456993305899991670] "" "Class ", 1071, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2952, 19543, 143514, 1156920, 10154697, 96374458, 983187204, 10727827066, 124649776016, 1536441262850, 20022556261395, 275040581877513, 3971718632568791, 60146544228837727] "" "Class ", 1072, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 1073, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 1074, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2979, 19946, 148750, 1222751, 10984400, 107061127, 1125200369, 12684426158, 152670671988, 1954029215315, 26500098881458, 379599290747541, 5727021619802183, 90770393077470174] "" "Class ", 1075, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 1076, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 1077, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 1078, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 564, 3655, 27014, 224784, 2077426, 21123549, 234291504, 2815309156, 36431041424, 505108309635, 7470062047216, 117379903416816, 1952928926660772, 34297339281052519, 634031331573675632] "" "Class ", 1079, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3218, 22357, 173517, 1486916, 13937443, 141805137, 1556035763, 18314276568, 230120186073, 3074185036783, 43505698535060, 650146837102797, 10230175238297626, 169061235502467251] "" "Class ", 1080, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1081, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1082, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 521, 3160, 21642, 165481, 1396263, 12893602, 129313706, 1400016787, 16272766267, 202124838695, 2671845112621, 37451329552072, 554854242814308, 8663453497595568, 142189831140530921] "" "Class ", 1083, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 490, 2775, 17307, 117414, 858109, 6704984, 55669340, 488648513, 4515345655, 43764835898, 443549513262, 4687683942514, 51538661683224, 588224911846667, 6956078577022724] "" "Class ", 1084, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1085, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1086, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 566, 3662, 27061, 224993, 2078516, 21121426, 234141599, 2811874439, 36366238759, 503922619184, 7448314336304, 116971771235110, 1945036400283346, 34139369182912893, 630753464205144614] "" "Class ", 1087, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 524, 3184, 21827, 166583, 1400381, 12854133, 127899440, 1371069746, 15751878973, 193067161503, 2514524400609, 34677348586323, 504799349817701, 7734944043704432, 124441323001243219] "" "Class ", 1088, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1089, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1090, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 526, 3230, 22507, 175511, 1514263, 14321140, 147319785, 1637606060, 19560915750, 249859929654, 3398552343614, 49041351151796, 748281403134735, 12036972929726924, 203593888294015099] "" "Class ", 1091, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2801, 17582, 120102, 884015, 6956945, 58171684, 514171308, 4783450433, 46668919048, 475997547828, 5061593537294, 55980259082033, 642578533503612, 7640805267748043] "" "Class ", 1092, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1093, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1094, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 543, 3437, 24857, 202223, 1827909, 18174666, 197135814, 2316468514, 29313779920, 397448100168, 5748012945617, 88325068860123, 1437056404713787, 24679976392298989, 446161467410349621] "" "Class ", 1095, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 497, 2906, 19107, 139530, 1120497, 9812848, 93059863, 949980365, 10385240884, 121039611834, 1498122256424, 19623371674981, 271187505884957, 3943098479030676, 60172500304734945] "" "Class ", 1096, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 1097, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 1098, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3075, 20881, 158195, 1322759, 12099189, 120169479, 1287845921, 14812342195, 181988106781, 2378723066599, 32957687057573, 482486792480495, 7441836061073932, 120618846958945964] "" "Class ", 1099, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 1100, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 1101, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 1102, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 544, 3443, 24896, 202585, 1831938, 18223780, 197775486, 2325274228, 29441618946, 399403742253, 5779509295892, 88858407331685, 1446537049376002, 24856596168652706, 449603970046709818] "" "Class ", 1103, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3140, 21600, 165952, 1408671, 13090016, 132163406, 1440565497, 16858959611, 210833494862, 2805811838507, 39591045205455, 590395553052881, 9277552843793502, 153225749674547997] "" "Class ", 1104, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1105, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1106, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 497, 2890, 18819, 135670, 1073196, 9246574, 86222350, 865340302, 9301670534, 106626062252, 1298451174325, 16740177889618, 227790221853357, 3262522073387253, 49060711032158180] "" "Class ", 1107, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2582, 15598, 102198, 719641, 5406832, 43093220, 362612679, 3208520184, 29751826538, 288265778631, 2910912850516, 30566114703638, 333083865298042, 3759999180988345] "" "Class ", 1108, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1109, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 0]]} "Class ", 1110, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 544, 3456, 25105, 205146, 1862649, 18603309, 202691598, 2392458701, 30411494419, 414184869470, 6016992486568, 92873889608682, 1517858831926358, 26184858289757082, 475494466891590158] "" "Class ", 1111, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2937, 19483, 143743, 1167056, 10335992, 99126164, 1023146865, 11306630307, 133173540220, 1665275675975, 22031013443203, 307416711629656, 4512012832302808, 69484422095825858] "" "Class ", 1112, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1113, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1114, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2920, 19258, 140991, 1133939, 9934306, 94137903, 959156020, 10454481389, 121363833366, 1494776793313, 19466459064331, 267243953200499, 3857123825807745, 58384173242955331] "" "Class ", 1115, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2364, 13485, 82729, 541809, 3764595, 27609915, 212838184, 1718408160, 14486981219, 127193836826, 1160368693560, 10977141603794, 107488849963632, 1087717826144528] "" "Class ", 1116, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1117, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1118, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 547, 3493, 25520, 209728, 1914989, 19233507, 210733070, 2501331394, 31973836507, 437906870097, 6397312011460, 99298386481372, 1631963463269049, 28311296775904559, 516993983436765106] "" "Class ", 1119, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2921, 19181, 139496, 1112607, 9655449, 90555845, 912668199, 9836363080, 112882680152, 1374247406336, 17689039999057, 240025695528977, 3424277627692033, 51238124758131491] "" "Class ", 1120, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 504, 3018, 20458, 154751, 1291490, 11782273, 116609514, 1244006028, 14227300786, 173615298257, 2251311589394, 30909855227449, 447900725943122, 6830443324813651, 109341125119924082] "" "Class ", 1121, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2590, 15762, 104509, 748291, 5744484, 47001567, 407823241, 3736457362, 36012817194, 363955397599, 3845804384569, 42380812701502, 485968970955841, 5786556693304716] "" "Class ", 1122, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {[0, 1, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 2997, 20182, 151494, 1253645, 11335787, 111178749, 1175403352, 13324273993, 161211867592, 2073495226310, 28250269927898, 406431030086258, 6157013713839112, 97964397331377726] "" "Class ", 1123, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 1124, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2617, 16166, 109386, 802340, 6325978, 53244908, 475707996, 4490010684, 44590663444, 464325010970, 5054425896806, 57364671174327, 677211702413791, 8298642664226318] "" "Class ", 1125, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 1126, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 495, 2877, 18768, 135777, 1078435, 9327363, 87246828, 877478889, 9441571899, 108213634419, 1316107388974, 16928010918387, 229572231170379, 3273859769207031, 48974663204901240] "" "Class ", 1127, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1128, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1129, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2962, 19880, 149096, 1236562, 11237613, 111069380, 1186214582, 13614233096, 167106966613, 2184468581331, 30299351503328, 444451991241280, 6874431886678368, 111818767773973757] "" "Class ", 1130, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2334, 13159, 79580, 512691, 3497978, 25153948, 189878783, 1499525100, 12353074347, 105888072700, 942352825279, 8690215383224, 82898522966168, 816748782276860] "" "Class ", 1131, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2562, 15481, 101768, 721455, 5475339, 44220892, 378167653, 3409939981, 32302778560, 320477333792, 3320644867516, 35847437134569, 402312305390041, 4684838712234418] "" "Class ", 1132, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 430, 2117, 10951, 58926, 327553, 1870804, 10933745, 65177731, 395272769, 2433595404, 15184467648, 95878345932, 611898247351, 3942956932504, 25630617521913] "" "Class ", 1133, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 556, 3568, 26175, 215986, 1980273, 19971523, 219726751, 2618889896, 33615207466, 462293356544, 6781538147768, 105698224232753, 1744338470898864, 30386096983009469, 557179943869253695] "" "Class ", 1134, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 521, 3139, 21295, 160605, 1333200, 12080263, 118649033, 1255635130, 14243991235, 172430087759, 2218647820920, 30236742863680, 435106274177933, 6592521417376142, 104907151466986798] "" "Class ", 1135, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 1136, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 1137, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 527, 3245, 22681, 177392, 1534660, 14549392, 149991519, 1670503024, 19987898588, 255702693926, 3482773208308, 50318471894813, 768622263191328, 12376679947083431, 209532780200006751] "" "Class ", 1138, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2801, 17582, 120102, 884015, 6956945, 58171684, 514171308, 4783450433, 46668919048, 475997547828, 5061593537294, 55980259082033, 642578533503612, 7640805267748043] "" "Class ", 1139, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 1140, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 1141, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3416, 24582, 198930, 1788362, 17683776, 190753330, 2229082960, 28051956844, 378235775186, 5439894232918, 83127960830348, 1345015646169446, 22971461239827600, 412977408588558078] "" "Class ", 1142, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2945, 19643, 146067, 1198002, 10742732, 104552449, 1097510251, 12359802308, 148636154129, 1900992811321, 25764383316461, 368854437869316, 5562171516368359, 88119006841104419] "" "Class ", 1143, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 1144, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 1145, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3075, 20881, 158195, 1322759, 12099189, 120169479, 1287845921, 14812342195, 181988106781, 2378723066599, 32957687057573, 482486792480495, 7441836061073932, 120618846958945964] "" "Class ", 1146, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 461, 2462, 14287, 89215, 594849, 4208018, 31416881, 246469080, 2024338552, 17353055345, 154840128433, 1434831998363, 13779917895329, 136911150816392, 1405010261639013] "" "Class ", 1147, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 1148, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 1149, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 546, 3472, 25230, 206244, 1873200, 18714780, 203973246, 2408372586, 30623784622, 417212460990, 6062955877638, 93613931310368, 1530453507767910, 26410759737930372, 479753379055248590] "" "Class ", 1150, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 2995, 20178, 151817, 1262298, 11495373, 113813314, 1217315284, 13988872158, 171895061904, 2249234871781, 31224419027092, 458370954126792, 7094568955788856, 115470619669251878] "" "Class ", 1151, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 1152, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 1153, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 1, 2, 3, 5], {1, 2}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3}, {}], [[5, 2, 3, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2973, 19822, 146859, 1196113, 10617687, 101998761, 1054055682, 11657766480, 137381802273, 1718396248011, 22735960802786, 317233284011051, 4655183456306522, 71667402477855999] "" "Class ", 1154, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2582, 15598, 102198, 719641, 5406832, 43093220, 362612679, 3208520184, 29751826538, 288265778631, 2910912850516, 30566114703638, 333083865298042, 3759999180988345] "" "Class ", 1155, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 1156, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 1157, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 545, 3465, 25179, 205804, 1869106, 18673484, 203515202, 2402872464, 30552768095, 416229622854, 6048452299370, 93386588529905, 1526680980019270, 26344696396170024, 478535865489954446] "" "Class ", 1158, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2973, 19951, 149272, 1231586, 11106215, 108660721, 1146251037, 12967976135, 156618766730, 2011128698283, 27359742446384, 393082150318738, 5947319052300182, 94518268045463767] "" "Class ", 1159, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1160, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1161, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2920, 19258, 140991, 1133939, 9934306, 94137903, 959156020, 10454481389, 121363833366, 1494776793313, 19466459064331, 267243953200499, 3857123825807745, 58384173242955331] "" "Class ", 1162, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2544, 15262, 99469, 698048, 5236972, 41756441, 352125985, 3127622638, 29156683342, 284405705746, 2894996738489, 30678599691391, 337738864542149, 3855311789013209] "" "Class ", 1163, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1164, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]} "Class ", 1165, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 506, 3044, 20747, 158001, 1329674, 12252319, 122689611, 1326569046, 15403231833, 191157644671, 2525046634668, 35371562486047, 523761198864782, 8174125280620711, 134103327844482800] "" "Class ", 1166, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 3, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 507, 3069, 21078, 161721, 1369713, 12684737, 127446452, 1380168591, 16020961793, 198394378375, 2610103084910, 36349385037169, 534137368386809, 8258144302287891, 133989487069900724] "" "Class ", 1167, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2644, 16421, 111595, 821299, 6491942, 54744866, 489772961, 4627060650, 45978378114, 478915530532, 5213537538533, 59162037271701, 698215347354025, 8552212693453989] "" "Class ", 1168, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}], [[4, 1, 2, 3, 5], {1, 2}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3}, {}], [[5, 2, 3, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 508, 3070, 20956, 159412, 1336885, 12249407, 121717222, 1303426375, 14962308798, 183267794629, 2385615355737, 32885163443397, 478537482001083, 7330338327169452, 117902361581562587] "" "Class ", 1169, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 2}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2440, 14245, 89429, 598308, 4237015, 31592261, 246963961, 2016935609, 17158392155, 151669401094, 1390002926644, 13182799854845, 129165772840628, 1305532088549506] "" "Class ", 1170, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {2}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 1, 5], {3, 4}, {}], [[3, 2, 4, 5, 1], {3}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 1, 2, 3, 5], {2}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {2}, {}], [[4, 2, 3, 5, 1], {2}, {}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3}, {}], [[5, 2, 3, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2662, 16638, 113886, 844493, 6726021, 57143345, 514952321, 4899127404, 49010742716, 513808774750, 5628114044279, 64246316420075, 762537814830323, 9391073140746735] "" "Class ", 1171, " is:" {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {2}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {2}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2213, 11950, 67789, 400232, 2442279, 15321356, 98405468, 644967576, 4302372679, 29147079932, 200182588326, 1391732208731, 9782219481989, 69439440751749] "" "Class ", 1172, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 556, 3342, 22452, 166516, 1350290, 11877550, 112591660, 1143797240, 12393295866, 142634281496, 1737352222867, 22324860927565, 301779071497298, 4280353124845886, 63556488122602123] "" "Class ", 1173, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 104, 542, 3186, 20799, 148915, 1158196, 9709783, 87189924, 834135461, 8463471773, 90719424424, 1023782536221, 12127316534351, 150387770567306, 1947672279988684, 26287183325533496] "" "Class ", 1174, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 3, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2, 4}, {}], [[2, 5, 3, 4, 1], {2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 103, 522, 2928, 17896, 117724, 825588, 6125890, 47802373, 390347903, 3321938776, 29360845212, 268724048775, 2540438588659, 24752743379132, 248094861393476, 2553629697291595] "" "Class ", 1175, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 509, 3011, 20024, 147824, 1200075, 10629881, 102038246, 1055370242, 11702113563, 138490513537, 1742506603018, 23228261788198, 327035654184287, 4849461729684689, 75546203830200752] "" "Class ", 1176, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2580, 15698, 104297, 750323, 5804384, 48003679, 422334113, 3935974823, 38712810160, 400545457105, 4347055178977, 49359698018586, 585041521350771, 7223349099012578] "" "Class ", 1177, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1178, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1179, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2591, 15778, 104710, 750630, 5771350, 47316453, 411638391, 3784368888, 36635309881, 372296963735, 3960760794618, 44006498684669, 509524290913288, 6135888679961332] "" "Class ", 1180, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2250, 12426, 73013, 452880, 2947354, 20027743, 141532541, 1036743360, 7849965066, 61293251049, 492508378609, 4065294546366, 34416181099282, 298413198893878] "" "Class ", 1181, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1182, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1183, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 521, 3157, 21646, 165905, 1406368, 13070349, 132178698, 1445220866, 16990011579, 213717841161, 2864396106205, 40751384319910, 613366326594264, 9737982357276326, 162638072940753001] "" "Class ", 1184, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2942, 19694, 147732, 1228344, 11220195, 111707274, 1204127143, 13971897184, 173643664647, 2301321803030, 32399214777872, 482882209461946, 7595705721462586, 125753594421339586] "" "Class ", 1185, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 1186, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 1187, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 483, 2748, 17446, 122273, 938102, 7823564, 70499995, 682889212, 7077978237, 78182744041, 917039480117, 11384977385684, 149166533424445, 2057084582809406, 29786817986463052] "" "Class ", 1188, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2534, 15149, 98339, 687429, 5140333, 40887142, 344311424, 3057074136, 28516774146, 278594818038, 2842624084703, 30218146407876, 333933055002313, 3828531897765942] "" "Class ", 1189, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 1190, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 1191, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3035, 20383, 152463, 1257802, 11348330, 111167802, 1175136713, 13333311356, 161625796525, 2084653681577, 28506184575034, 411935917533132, 6272689803427745, 100388401549762802] "" "Class ", 1192, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2580, 15698, 104297, 750323, 5804384, 48003679, 422334113, 3935974823, 38712810160, 400545457105, 4347055178977, 49359698018586, 585041521350771, 7223349099012578] "" "Class ", 1193, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 1194, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 1195, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 483, 2745, 17406, 121854, 934063, 7786257, 70162372, 679908668, 7053037065, 78001862247, 916320517429, 11396525121334, 149619078319645, 2067847648451113, 30012371134538906] "" "Class ", 1196, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 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]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2233, 12225, 70955, 433205, 2765501, 18372536, 126538279, 900678596, 6608068215, 49862196675, 386218603617, 3065791381859, 24904158746628, 206760206185056] "" "Class ", 1197, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 1198, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 1199, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 506, 2986, 19788, 145706, 1180246, 10434364, 99989524, 1032487078, 11429541746, 135033822134, 1695946163310, 22564073692266, 317031445647256, 4690816793080062, 72904840384178702] "" "Class ", 1200, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 462, 2492, 14664, 93361, 637965, 4654636, 36086710, 296188860, 2564938255, 23367211158, 223356156531, 2234626164264, 23348892029196, 254274330918983, 2880743550721514] "" "Class ", 1201, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 1202, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 1203, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 490, 2803, 17805, 124603, 950394, 7855749, 69879128, 666026125, 6767937131, 73071458513, 835083146488, 10073756860196, 127892745359480, 1704879458282608, 23806368355683107] "" "Class ", 1204, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2336, 13104, 78288, 493896, 3270472, 22615464, 162670152, 1212975904, 9350571488, 74340383776, 608312875552, 5114065847104, 44102540457408, 389595453153216] "" "Class ", 1205, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 1206, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 1207, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2568, 15576, 103182, 740397, 5716670, 47222740, 415299192, 3871829158, 38123720561, 395156396512, 4299045933023, 48963915747594, 582464703836334, 7221710409619094] "" "Class ", 1208, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2651, 16605, 114779, 867980, 7129670, 63223292, 602068543, 6128740743, 66418532698, 763535093799, 9280804247622, 118930509980614, 1602533811517725, 22650959714980647] "" "Class ", 1209, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2257, 12551, 74594, 470119, 3122832, 21753774, 158259887, 1198209554, 9413003398, 76531054975, 642523870652, 5559388380229, 49487380509383, 452497818881806] "" "Class ", 1210, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1211, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1212, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1213, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2883, 18751, 134961, 1065152, 9149434, 84993441, 849197627, 9082048190, 103533237085, 1253345198900, 16058513938341, 217110518537588, 3089030898550135, 46138650474021140] "" "Class ", 1214, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622] "" "Class ", 1215, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2700, 16814, 114664, 848512, 6765260, 57768768, 525682800, 5075846520, 51813669604, 557340819172, 6299377996536, 74622058842652, 924354649697852, 11948579980034870] "" "Class ", 1216, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622] "" "Class ", 1217, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "Class ", 1218, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 1219, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "Class ", 1220, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 1221, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2931, 19394, 142895, 1161309, 10326085, 99753177, 1040567173, 11658649148, 139646092659, 1780819652606, 24089794925136, 344549804834325, 5195255542428477, 82367045039875030] "" "Class ", 1222, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2544, 15724, 107560, 807460, 6604272, 58481736, 557586772, 5696365056, 62089168564, 719305384456, 8826996890344, 114390029929136, 1561140505037492, 22381525703836584] "" "Class ", 1223, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1224, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1225, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1226, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1227, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1228, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1229, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3106, 21351, 164431, 1402149, 13116705, 133549367, 1470224479, 17401422259, 220354382209, 2972595845866, 42559068078616, 644522562398257, 10293822573375090, 172918473955747634] "" "Class ", 1230, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2983, 20147, 152393, 1276689, 11738504, 117536551, 1273253791, 14838132285, 185112547456, 2461600489589, 34759817983538, 519458884115028, 8190848053164896, 135903938622590989] "" "Class ", 1231, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1232, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1233, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1234, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1235, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1236, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1237, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3165, 21652, 165131, 1389939, 12800766, 128038503, 1382347404, 16022189757, 198437805178, 2615429688434, 36551177830562, 539879570930174, 8403740546556269, 137497957989811841] "" "Class ", 1238, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 487, 2806, 18116, 129566, 1016582, 8682931, 80201049, 796538639, 8464907308, 95843201907, 1151813046031, 14642949868964, 196335597979418, 2769003262883149, 40977427852866462] "" "Class ", 1239, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 1240, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 1241, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 1242, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 1243, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 1244, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 1245, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 518, 3121, 21169, 160212, 1336027, 12187077, 120631577, 1288367511, 14763871984, 180725694650, 2353350833705, 32484471660428, 473782308685362, 7280562713282787, 117572038246033493] "" "Class ", 1246, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 479, 2688, 16699, 113664, 839995, 6691752, 57111479, 519482414, 5013327403, 51132740403, 549296701506, 6196453157456, 73205764378448, 903594800902184, 11627666089606782] "" "Class ", 1247, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1248, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1249, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1250, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1251, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1252, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1253, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 528, 3254, 22750, 177888, 1538219, 14574428, 150154866, 1671271025, 19984992464, 255519059013, 3478402253489, 50230115538647, 766914220821475, 12343808323648695, 208891726111741845] "" "Class ", 1254, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 487, 2817, 18276, 131393, 1036550, 8901034, 82643036, 824908574, 8808442863, 100189696262, 1209313524904, 15438108429380, 207822193537231, 2942168785432905, 43698730838081756] "" "Class ", 1255, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1256, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1257, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1258, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1259, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1260, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1261, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2931, 19368, 142269, 1150767, 10166281, 97414567, 1006396030, 11151765405, 131940460402, 1660114887171, 22135377924810, 311783301067822, 4625991778105486, 72116079298693114] "" "Class ", 1262, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 94, 454, 2432, 14268, 90828, 622916, 4575878, 35828968, 297766066, 2616874246, 24239361266, 235941588084, 2407005436648, 25674173721234, 285706100666478, 3310471625269442] "" "Class ", 1263, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 1264, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 1265, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 1266, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 1267, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 1268, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 1269, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2914, 19142, 139576, 1119285, 9795138, 92925221, 950181133, 10419224729, 121979946251, 1518636109859, 20035839340859, 279245657843470, 4099816216233177, 63246087227588011] "" "Class ", 1270, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2635, 16419, 112751, 846018, 6886230, 60433245, 568815423, 5715890118, 61075517281, 691481547453, 8268923873611, 104145793473794, 1377995515025179, 19110047149233282] "" "Class ", 1271, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1272, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1273, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1274, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1275, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1276, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 0]]} "Class ", 1277, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2922, 19327, 142320, 1155147, 10246803, 98628599, 1023826056, 11401704550, 135594665721, 1715127448162, 22992380851225, 325631417855008, 4858327780895675, 76164085947053868] "" "Class ", 1278, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[1, 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, 6, 22, 94, 454, 2432, 14268, 90828, 622916, 4575878, 35828968, 297766066, 2616874246, 24239361266, 235941588084, 2407005436648, 25674173721234, 285706100666478, 3310471625269442] "" "Class ", 1279, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1280, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1281, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1282, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1283, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1284, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1285, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 507, 3067, 21049, 161578, 1371706, 12761821, 129123856, 1411679822, 16584064053, 208345297712, 2787324099576, 39563123123002, 593827752846631, 9397571979797337, 156387794080930309] "" "Class ", 1286, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 462, 2577, 16108, 111652, 850305, 7059867, 63479417, 614578744, 6374667756, 70528696593, 829126674185, 10321171214310, 135629650094010, 1876279831954845, 27256696130822386] "" "Class ", 1287, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 464, 2620, 16722, 119216, 939454, 8109750, 76106244, 771424570, 8398533584, 97734745812, 1210577352702, 15900641755900, 220738337887226, 3229219602914246, 49650079652227832] "" "Class ", 1288, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 432, 2260, 13063, 82674, 567987, 4203509, 33289659, 280523773, 2503157312, 23553422863, 232861656516, 2411289150000, 26079647737952, 293890998577844, 3443098651761956] "" "Class ", 1289, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "Class ", 1290, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 1291, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "Class ", 1292, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 1293, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2523, 15583, 106867, 806562, 6646236, 59381203, 571828343, 5904365869, 65073384102, 762474455187, 9464663047755, 124072469443344, 1712811531576830, 24837131010818514] "" "Class ", 1294, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2533, 15639, 107009, 804280, 6588118, 58411626, 557245413, 5690706029, 61931405852, 715435638424, 8742480887088, 112657316086442, 1526659641668417, 21702045801000509] "" "Class ", 1295, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3}, { [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2191, 12380, 76524, 513447, 3711793, 28722411, 236577366, 2064231686, 19001305690, 183861513416, 1864304298702, 19754130541338, 218195031738529, 2506810233287998] "" "Class ", 1296, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1297, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1298, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1299, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 519, 3173, 22004, 170622, 1463293, 13752400, 140571251, 1552645791, 18429262206, 233945167538, 3162755593695, 45367965583782, 688226957261426, 11008534585329143, 185177442466645406] "" "Class ", 1300, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 487, 2809, 18174, 130236, 1024033, 8764843, 81117532, 807171922, 8593324845, 97462885645, 1173172768388, 14937385732490, 200575725793229, 2832734084058687, 41976081892427997] "" "Class ", 1301, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 1302, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 1303, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 490, 2874, 19102, 142054, 1170050, 10579634, 104240534, 1111963182, 12770690594, 157137340070, 2062604990558, 28771481841762, 425046951675466, 6629952551184586, 108889155586666806] "" "Class ", 1304, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2498, 15022, 98418, 695842, 5268878, 42460214, 362281270, 3258411994, 30777752362, 304322755790, 3141041028250, 33757975674802, 376952492567638, 4364658808619958] "" "Class ", 1305, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 1306, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 1307, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2952, 19587, 144552, 1174934, 10432474, 100484353, 1043612748, 11626495655, 138309572934, 1749893094558, 23463137146779, 332354415298477, 4959342612716685, 77757282023313230] "" "Class ", 1308, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 461, 2565, 16013, 110971, 845676, 7030290, 63319310, 614234206, 6384886021, 70804362403, 834359188627, 10411754984215, 137159716501614, 1902184313616042, 27702013236544102] "" "Class ", 1309, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 1310, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 1311, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2624, 16200, 109569, 804673, 6369554, 54010335, 488030039, 4677975379, 47381737535, 505378697618, 5659302871928, 66356385766234, 812706342767052, 10374760032219828] "" "Class ", 1312, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2157, 11844, 70021, 442767, 2977019, 21175262, 158642220, 1247179151, 10255630512, 87964260420, 785049605633, 7274361387377, 69849355884564, 693823728839137] "" "Class ", 1313, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 1314, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 1315, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 2993, 20113, 150685, 1246016, 11272675, 110773397, 1174952482, 13380113859, 162822482477, 2108655200564, 28956974309359, 420295702671110, 6429118602523787, 103373650626794319] "" "Class ", 1316, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2540, 15626, 105994, 785958, 6325138, 54907176, 511425284, 5087826926, 53842565626, 603962663246, 7158165556678, 89384005652578, 1172911600292766, 16136298607932164] "" "Class ", 1317, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 1318, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 1319, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2517, 15284, 101679, 734557, 5720773, 47733740, 424464621, 4004255049, 39916338793, 419015540851, 4617883733611, 53287114132936, 642282990290133, 8069010153961581] "" "Class ", 1320, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2148, 11647, 67275, 410843, 2636849, 17699199, 123746381, 898155393, 6747868807, 52349013907, 418457779333, 3440216859604, 29040046554184, 251334398109988] "" "Class ", 1321, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 1322, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 1323, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2973, 19888, 148253, 1218514, 10951286, 106833309, 1124350486, 12698400932, 153192731767, 1966127875673, 26749163726954, 384543112649468, 5824671282969951, 92718567140252932] "" "Class ", 1324, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 461, 2565, 16013, 110971, 845676, 7030290, 63319310, 614234206, 6384886021, 70804362403, 834359188627, 10411754984215, 137159716501614, 1902184313616042, 27702013236544102] "" "Class ", 1325, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1326, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1327, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2514, 15394, 104141, 772205, 6232749, 54430260, 511623626, 5152314615, 55362207320, 632398990037, 7654218934403, 97869197183257, 1318406495544689, 18665410784462606] "" "Class ", 1328, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}] , [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[1, 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, 6, 22, 92, 428, 2198, 12370, 75695, 499881, 3539044, 26707736, 213786319, 1807444684, 16079872593, 150044860235, 1464313966684, 14907823822625, 157968752730475, 1738662184950632] "" "Class ", 1329, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1330, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]} "Class ", 1331, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {3}, {}], [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 461, 2565, 16003, 110735, 841740, 6971264, 62468348, 602054812, 6208892615, 68211794119, 795201580241, 9803251861013, 127410930714206, 1740983449189514, 24949432172627538] "" "Class ", 1332, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2152, 11729, 68355, 422784, 2758310, 18885664, 135128242, 1006765880, 7786708488, 62356006287, 515830491203, 4399127111486, 38608663873516, 348156150091432] "" "Class ", 1333, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 464, 2616, 16589, 116903, 906223, 7662401, 70171132, 691858863, 7306418156, 82276935197, 984091458543, 12458647420236, 166434720447085, 2339662271938428, 34523566909450249] "" "Class ", 1334, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 2000, 10378, 56967, 328606, 1981326, 12432794, 80901370, 544271046, 3776130912, 26959412016, 197693451038, 1486562112777, 11446119455151, 90128897405143] "" "Class ", 1335, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[3, 2, 4, 1, 5], {3, 4}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 429, 2221, 12689, 79357, 538652, 3937548, 30792888, 256177402, 2256438951, 20956562983, 204497961275, 2090174435759, 22315793593422, 248269278296954, 2871911317630138] "" "Class ", 1336, " is:" {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 392, 1790, 8510, 41908, 212752, 1108680, 5909089, 32115621, 177551485, 996463118, 5667495146, 32620847623, 189779109361, 1114811487678, 6606434207811] "" "Class ", 1337, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1338, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 2, 4, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1339, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {2, 3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}], [[4, 1, 5, 2, 3], {2, 3}, {}], [[4, 1, 5, 3, 2], {1, 2, 3}, {}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3157, 21475, 162253, 1347311, 12192736, 119384034, 1257164815, 14164480720, 169991969709, 2164612960617, 29144735702782, 413655073163511, 6171995294320103, 96571992570747031] "" "Class ", 1340, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1341, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1342, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1343, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2753, 17406, 120884, 913542, 7456094, 65313004, 610811532, 6071318655, 63890825897, 709411192833, 8286288483820, 101547006968565, 1302515525399269, 17449122272124900] "" "Class ", 1344, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2407, 13891, 86140, 569387, 3987165, 29434781, 228185636, 1851551705, 15682539164, 138329087162, 1268068825870, 12059335823995, 118783601816792, 1210067805657206] "" "Class ", 1345, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1346, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1347, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 1348, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [ [2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2769, 17704, 125085, 967457, 8128823, 73715837, 717511502, 7460153639, 82509403862, 967156172849, 11975949112720, 156198526869970, 2140227576183231, 30734840694649372] "" "Class ", 1349, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 1350, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 1351, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {}, {}], [[3, 1, 4, 2, 5], {2, 3}, {}], [[3, 1, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {2, 3}, {}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2636, 16289, 110115, 806947, 6363863, 53688529, 482121465, 4588878697, 46126860868, 488122540750, 5422902068584, 63096137825868, 767182115407721, 9729113246246890] "" "Class ", 1352, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 1353, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 1354, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 1355, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3067, 20630, 154094, 1264467, 11303337, 109296912, 1136331752, 12637902158, 149688940550, 1880886498840, 24986522394992, 349861875568207, 5149334751583109, 79470048332307376] "" "Class ", 1356, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 1357, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 1358, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 1359, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2659, 16616, 114111, 853592, 6904989, 60044688, 558475053, 5532052684, 58144327437, 646325475884, 7576418306332, 93416575795908, 1208704828015728, 16377015711574225] "" "Class ", 1360, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2145, 11600, 66785, 406702, 2606803, 17518561, 123056064, 901196354, 6866301833, 54327694998, 445679423760, 3785396093634, 33245385391133, 301559729062740] "" "Class ", 1361, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 1362, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 1363, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 1364, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 1365, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 1366, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 1367, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {2, 3}, {}], [[3, 1, 5, 2, 4], {2, 3}, {}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {2, 3}, {}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[3, 2, 5, 4, 1], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 2, 3], {2, 3}, {}], [[4, 1, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 497, 2899, 18934, 136795, 1082467, 9306664, 86354715, 859855998, 9143091077, 103383147491, 1238463923698, 15666383244837, 208658588946131, 2918419101322110, 42763799684268093] "" "Class ", 1368, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 1369, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 1370, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 1371, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [ [1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [ [2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [ [3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}] , [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [ [4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2634, 16263, 109841, 804115, 6334669, 53382249, 478817679, 4552109261, 45703682666, 483081307362, 5360731496394, 62302586537288, 756703432304891, 9586053840409652] "" "Class ", 1372, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1373, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2157, 11706, 67630, 413192, 2656205, 17896637, 125988317, 924351442, 7053011479, 55867822274, 458690899108, 3898064601293, 34245810827118, 310671092130604] "" "Class ", 1374, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[2, 4, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 1, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 1, 5, 2, 4], {2, 3}, {}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 4, 1, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[3, 2, 5, 4, 1], {4}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 1, 5, 2, 3], {2, 3}, {}], [[4, 1, 5, 3, 2], {1}, {}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 2, 5, 3, 1], {1}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 445, 2357, 13635, 85175, 569751, 4052944, 30489294, 241430982, 2004505801, 17391602325, 157231447644, 1477471680153, 14398747567903, 145249006426429, 1514031162859542] "" "Class ", 1375, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 1, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 1981, 10041, 52970, 288669, 1616081, 9254678, 54030668, 320730812, 1931627582, 11781966272, 72674770935, 452776410482, 2846183807089, 18035668933355] "" "Class ", 1376, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "Class ", 1377, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [ [3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2668, 16426, 110340, 801768, 6258920, 52203072, 463061040, 4351616246, 43181141388, 451149799142, 4950320160844, 56918827359398, 684404161243228, 8590321350191806] "" "Class ", 1378, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 3}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 3}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 508, 3004, 19916, 146196, 1176184, 10285952, 97110136, 984055600, 10650151184, 122576202840, 1494643584256, 19244579125592, 260877315044032, 3713412963259768, 55371353528807696] "" "Class ", 1379, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 1380, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "Class ", 1381, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 1382, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2705, 16799, 113809, 833110, 6539444, 54698372, 484995516, 4538513884, 44653841990, 460414303856, 4960633167622, 55708793664726, 650625055350856, 7886476216592946] "" "Class ", 1383, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 1384, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 4, 2, 5], {2, 3}, {}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3069, 20656, 154391, 1267939, 11344189, 109792615, 1142596843, 12720487346, 150825821670, 1897233369297, 25231867730708, 353702062275920, 5211951910907041, 80532470539167411] "" "Class ", 1385, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1386, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1387, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1388, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1389, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 1, 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, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2160, 11745, 67951, 415158, 2663248, 17857591, 124697751, 904096911, 6789017570, 52689031367, 421867229075, 3479390487790, 29520255906055, 257345675155774] "" "Class ", 1390, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1391, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1392, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1393, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1394, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1395, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1396, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {3}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2470, 14747, 96127, 678868, 5161748, 42032630, 364915166, 3364430241, 32828638569, 337982779148, 3661483514090, 41637032421614, 495909930884188, 6173800127705605] "" "Class ", 1397, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2300, 13010, 79007, 511140, 3501498, 25273671, 191433548, 1516429762, 12526236293, 107628357447, 959830177946, 8867302814983, 84718862826378, 835796552472678] "" "Class ", 1398, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1399, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1400, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 4, 1, 5], {2, 3}, {}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {2, 3}, {}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 2987, 19937, 147669, 1201643, 10651425, 102115230, 1052526399, 11604339511, 136248145765, 1696993234683, 22345189114369, 310114695804817, 4523904174650119, 69197928574629765] "" "Class ", 1401, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 1402, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 1403, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 1404, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2536, 15524, 104346, 763634, 6043780, 51442202, 468652126, 4551064406, 46939621346, 512555819118, 5908442052288, 71714920594142, 914377548845992, 12220290321304186] "" "Class ", 1405, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 1406, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 1407, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 1408, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1409, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1410, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1411, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1412, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {2, 3}, {}], [[2, 5, 1, 3, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {2, 3}, {}], [[3, 4, 1, 2, 5], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2791, 18017, 128915, 1012081, 8646141, 79816270, 791521046, 8389480442, 94624756002, 1131369661734, 14291059933764, 190141992539807, 2657521445744811, 38923243779100739] "" "Class ", 1413, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 5, 1, 3, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 1414, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1415, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1416, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {2, 4}, {}], [[4, 1, 2, 3, 5], {2}, {}], [[4, 1, 2, 5, 3], {2, 3, 4}, {}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {2, 3, 4}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3176, 21737, 165540, 1387412, 12685644, 125610957, 1338704253, 15275526923, 185774848114, 2398444610162, 32756961008669, 471799901375513, 7146360057104102, 113552988521535314] "" "Class ", 1417, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2796, 17986, 127786, 993108, 8376496, 76177793, 742799507, 7728744855, 85453508809, 1000334430619, 12357998924829, 160651291833244, 2191934285278246, 31315678895110107] "" "Class ", 1418, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1419, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1420, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2772, 17760, 125856, 977016, 8244120, 75112776, 734797608, 7680478824, 85415240808, 1006904767752, 12540448110504, 164523883419528, 2267708178635304, 32760491425585608] "" "Class ", 1421, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 1422, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1423, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1424, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 1425, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [ [2, 3, 4, 1, 5], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2496, 15024, 98871, 705584, 5424432, 44675982, 392339956, 3658969559, 36109921136, 375935145816, 4117329578247, 47321399305106, 569465549805800, 7160839714241083] "" "Class ", 1426, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 1427, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 1428, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 1429, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 1430, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 1431, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 1432, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 2, 5], {2, 3}, {}], [[3, 1, 5, 2, 4], {2, 3}, {}], [[3, 1, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}], [[4, 1, 5, 2, 3], {2, 3}, {}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2973, 19788, 146243, 1187790, 10511489, 100641796, 1036315913, 11417730290, 134001511483, 1668755217372, 21975427519319, 305082516054158, 4452921184365509, 68163347551435908] "" "Class ", 1433, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1434, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1435, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1436, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2507, 15122, 99746, 713651, 5503099, 45486359, 401129962, 3758932078, 37296978127, 390610875662, 4305789471056, 49830839363826, 604066559110593, 7654327079879192] "" "Class ", 1437, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 431, 2210, 12245, 72601, 457298, 3042747, 21290484, 156084985, 1195279370, 9536623979, 79101297970, 680786811612, 6069522374448, 55972359776212, 533206449788920] "" "Class ", 1438, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1439, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 0]]} "Class ", 1440, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 2, 4, 5], {3, 4}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {3}, {}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 2, 5, 3], {3}, {}], [[1, 4, 3, 2, 5], {3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 1, 4, 5], {3, 4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 1, 5, 3], {3}, {}], [[2, 4, 3, 1, 5], {3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 1, 5, 2], {3}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2954, 19675, 145698, 1186774, 10541196, 101359682, 1048665154, 11612764611, 137024466963, 1715966049229, 22727697277817, 317391761733691, 4660459384284283, 71775237246380697] "" "Class ", 1441, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 3, 2, 5], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 3, 1, 5], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2499, 15077, 99581, 714153, 5523862, 45822069, 405682993, 3817376631, 38038472533, 400093353722, 4429299027512, 51478848776962, 626667850280556, 7973505690087828] "" "Class ", 1442, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1443, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1444, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {3}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 5, 2], {1, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2460, 14680, 95719, 676695, 5154064, 42062538, 366116749, 3385221275, 33133841904, 342236544976, 3720063604560, 42448736504323, 507334756796533, 6338022300453009] "" "Class ", 1445, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1976, 10091, 54278, 306135, 1804050, 11075338, 70660276, 467522296, 3202311234, 22671811571, 165683925951, 1248314022006, 9686133698873, 77328654525178] "" "Class ", 1446, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1447, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1448, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {}], [[2, 4, 1, 3], {1}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 4, 1, 5], {2, 3}, {}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}], [[4, 2, 5, 1, 3], {2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 3000, 20205, 151484, 1250406, 11263036, 109899715, 1154488649, 12987890069, 155760411744, 1983398737402, 26721986361403, 379730919652139, 5675687290426725, 89003094047119169] "" "Class ", 1449, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 1450, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 1451, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} "Class ", 1452, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2526, 15485, 104697, 774154, 6215033, 53836224, 500469204, 4969466672, 52490358704, 587627408537, 6949713666907, 86578715273078, 1133176231372287, 15545214682271158] "" "Class ", 1453, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 1454, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 1, 4], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1, 5], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2152, 11750, 68862, 430720, 2861342, 20103144, 148820608, 1157022326, 9419658012, 80096788066, 709692829298, 6538684761108, 62524642542970, 619447422539108] "" "Class ", 1455, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 1456, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1457, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1458, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [ [1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 3, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 408, 1947, 9809, 51943, 288219, 1671427, 10107221, 63602233, 415735257, 2818059619, 19779820215, 143561626558, 1076094468176, 8320539780991, 66293474863193] "" "Class ", 1459, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2154, 11783, 69229, 434196, 2892053, 20366649, 151063436, 1176176303, 9584801959, 81538537926, 722447948389, 6652931867962, 63558006823177, 628842940802953] "" "Class ", 1460, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [ [1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {}], [[3, 4, 1, 2, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 390, 1744, 7950, 36717, 171222, 804488, 3802964, 18068346, 86212596, 412873654, 1983576850, 9556451836, 46155130026, 223409492656, 1083533310394] "" "Class ", 1461, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {2, 4}, {}], [[4, 1, 2, 3, 5], {2}, {}], [[4, 1, 2, 5, 3], {2, 3, 4}, {}], [[4, 1, 3, 5, 2], {2, 3, 4}, {}], [[4, 2, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3087, 20965, 158426, 1317549, 11952105, 117403624, 1241081633, 14044823983, 169377204900, 2168166919293, 29356995094469, 419144951228860, 6292835930726646, 99100349119281999] "" "Class ", 1462, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {}], [ [3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 483, 2752, 17495, 122701, 940642, 7821951, 70099380, 673332550, 6899221069, 75098640039, 865269766541, 10518791139634, 134534646255014, 1805692218343043, 25374118551903696] "" "Class ", 1463, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 1464, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 1465, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {4, 5}, {}], [[1, 4, 5, 2, 3], {1, 2}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {4, 5}, {}], [[2, 4, 5, 1, 3], {1, 2}, {}], [[2, 4, 5, 3, 1], {4}, {}], [[3, 4, 5, 1, 2], {1, 2}, {}], [[3, 4, 5, 2, 1], {4}, {}], [[4, 1, 3, 2, 5], {1, 4}, {}], [[4, 2, 3, 1, 5], {1, 4}, {}], [[5, 1, 3, 2, 4], {4, 5}, {}], [[5, 1, 4, 2, 3], {2, 3}, {}], [[5, 1, 4, 3, 2], {4}, {}], [[5, 2, 3, 1, 4], {4, 5}, {}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 2, 4, 3, 1], {4}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2772, 17760, 125856, 977016, 8244120, 75112776, 734797608, 7680478824, 85415240808, 1006904767752, 12540448110504, 164523883419528, 2267708178635304, 32760491425585608] "" "Class ", 1466, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {4}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 1467, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 1468, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 1469, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 1470, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [ [2, 3, 5, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2523, 15435, 104101, 767613, 6143830, 53046628, 491445642, 4862567335, 51173446503, 570732551367, 6723912259238, 83435768714913, 1087648458911549, 14859504407555487] "" "Class ", 1471, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 1472, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 1473, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 1474, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {4}, {}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {}], [[4, 2, 3, 1, 5], {1, 4}, {[0, 0, 1, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2108, 11156, 62309, 365130, 2235400, 14252124, 94389503, 648028444, 4604053885, 33799970770, 256066777757, 1999596584937, 16077643963794, 132975124237508] "" "Class ", 1475, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 1476, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 1477, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 1478, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2510, 15325, 103309, 762920, 6129040, 53241183, 497429110, 4975151597, 53047275622, 600738716055, 7201490753994, 91109576047071, 1213176758370671, 16959918698034060] "" "Class ", 1479, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 1480, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 1481, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[1, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[1, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {[1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2514, 15239, 101201, 730145, 5683884, 47467376, 423178491, 4010399713, 40251206384, 426460717227, 4755846920817, 55679776798785, 682766060736089, 8750461740459164] "" "Class ", 1482, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 1483, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 1484, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 1485, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1486, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {3, 4}, {}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {3, 4}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 3, 4, 1, 5], {3, 4}, {}], [[2, 3, 5, 1, 4], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {3, 4}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {3, 4}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2526, 15493, 104871, 776709, 6248003, 54245287, 505537398, 5033290038, 53314577782, 598595118313, 7100489372984, 88722982080853, 1164741898475670, 16026257569633186] "" "Class ", 1487, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1488, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1489, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {3}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2486, 14947, 98346, 702441, 5410529, 44691184, 393987456, 3691692028, 36633447045, 383750400179, 4231554113879, 48991374685055, 594162036308192, 7532607325084283] "" "Class ", 1490, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {4}, {}], [[3, 4, 1, 5, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}], [[3, 5, 1, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2131, 11481, 66019, 403089, 2601897, 17689287, 126252919, 943260194, 7358147345, 59794051102, 505133081661, 4427960561371, 40208493721744, 377640531046772] "" "Class ", 1491, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1492, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "Class ", 1493, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4, 5], {4}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {4}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 4}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {}], [[2, 4, 3, 5, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 4}, {}], [[3, 2, 4, 5, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {4}, {}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {1, 4}, {}], [[4, 2, 3, 5, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {4}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 4}, {}], [[5, 2, 3, 4, 1], {1, 4}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2169, 11941, 70699, 447298, 3007784, 21397410, 160404502, 1262740511, 10407361555, 89564641605, 802917757117, 7482070034938, 72336731697514, 724322327760806] "" "Class ", 1494, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {2, 3, 4}, {}], [[3, 5, 1, 2, 4], {2, 3, 4}, {}], [[4, 5, 1, 2, 3], {3}, {}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 463, 2591, 16215, 112053, 846886, 6947100, 61457631, 583114625, 5905703918, 63581121732, 725004842753, 8727854888625, 110605382256511, 1471711558367257, 20513093131552841] "" "Class ", 1495, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1496, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[1, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[1, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 2, 4, 1, 5], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2184, 12096, 72104, 459440, 3111616, 22292592, 168263312, 1333377904, 11059335280, 95753379216, 863373139824, 8089902823120, 78625465178608, 791248858589264] "" "Class ", 1497, " is:" {{[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 1498, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 2, 3, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 103, 522, 2931, 17945, 118335, 832613, 6205281, 48701776, 400627666, 3440724054, 30749804378, 285168814687, 2737676671642, 27150213183041, 277637440280988, 2922752384167220] "" "Class ", 1499, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 103, 515, 2802, 16317, 100545, 650187, 4385192, 30700869, 222284747, 1659504511, 12744300805, 100477770076, 811960324446, 6716157741721, 56797769174397, 490618287650471] "" "Class ", 1500, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 3, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 2, 4, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1501, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 491, 2779, 17334, 117658, 860920, 6741335, 56149682, 494986553, 4598884568, 44869851668, 458289067281, 4886710837644, 54266872854179, 626265467805109, 7496344252063179] "" "Class ", 1502, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 452, 2395, 13783, 85246, 562138, 3927722, 28932343, 223753516, 1810445997, 15280552583, 134188165077, 1223308814168, 11554338006949, 112869555634292, 1138536338154126] "" "Class ", 1503, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1504, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 1]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2150, 11708, 68282, 423948, 2788230, 19341952, 141003552, 1076787624, 8589843716, 71404154928, 617151121998, 5535236798058, 51426766394244, 494145546973656] "" "Class ", 1505, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3, 4}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2407, 13884, 85934, 565671, 3932668, 28715394, 219216426, 1743120808, 14391460768, 123037620767, 1086734655049, 9896722374158, 92764112920628, 893547691053781] "" "Class ", 1506, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2091, 10951, 60145, 343858, 2035163, 12417465, 77849816, 500202046, 3286917766, 22051934900, 150836416463, 1050640719993, 7444851520152, 53621515807371] "" "Class ", 1507, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1508, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1509, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 490, 2773, 17305, 117614, 862574, 6775532, 56657662, 501815585, 4687469533, 46009258972, 473019991018, 5079579969117, 56835278217072, 661143302550059, 7980044997849215] "" "Class ", 1510, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2566, 15528, 102364, 728656, 5560837, 45229253, 390107345, 3552820745, 34039088543, 341974142587, 3592382426771, 39359427363375, 448758152310494, 5313656385685643] "" "Class ", 1511, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 1512, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 1513, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2408, 13921, 86638, 575985, 4066482, 30347999, 238522698, 1968270048, 17008706434, 153575132825, 1446044124204, 14173945108741, 144396173054757, 1526647669376953] "" "Class ", 1514, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2218, 12070, 69585, 422058, 2679436, 17734726, 122005416, 870229823, 6422542905, 48961810772, 384990627028, 3118385744399, 25989778243549, 222649708400129] "" "Class ", 1515, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 1516, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 1517, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2693, 16593, 111213, 803394, 6210498, 51074423, 444659725, 4081239915, 39349813019, 397308187705, 4189472384825, 46024254224324, 525620142427516, 6228352362204529] "" "Class ", 1518, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {2, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2284, 12830, 77205, 493870, 3338128, 23724294, 176573902, 1371581776, 11086959054, 93025658456, 808415300855, 7262108731120, 67318792260765, 642958524205018] "" "Class ", 1519, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 1520, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 2, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 1521, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2438, 14244, 89827, 606872, 4367080, 33320115, 268549245, 2279181687, 20313774541, 189676128663, 1851398387430, 18853227275806, 199925102616060, 2203919564037112] "" "Class ", 1522, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1971, 9970, 52542, 286392, 1605728, 9221360, 54059745, 322656058, 1956316523, 12027744424, 74871508789, 471281314080, 2996409355323, 19225253511378] "" "Class ", 1523, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 1524, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 2, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 1525, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2652, 16130, 106237, 750918, 5655236, 45115447, 379422561, 3350242607, 30950953609, 298269667652, 2990471132172, 31121449512994, 335487967133454, 3739325911364885] "" "Class ", 1526, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2222, 12144, 70552, 432932, 2792706, 18865924, 133047698, 976854832, 7449078797, 58869859832, 481242665301, 4062204347857, 35351286792391, 316722297329545] "" "Class ", 1527, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 1528, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1809, 8613, 42210, 211779, 1083378, 5632808, 29691276, 158352356, 853127648, 4636920320, 25398300249, 140071996831, 777220526035, 4336186086677] "" "Class ", 1529, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2492, 14564, 91356, 609555, 4296324, 31810475, 246296300, 1986631847, 16640285030, 144344680839, 1293629017335, 11953351735253, 113670798764789, 1110667828214216] "" "Class ", 1530, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 1531, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 1532, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1809, 8613, 42210, 211779, 1083378, 5632808, 29691276, 158352356, 853127648, 4636920320, 25398300249, 140071996831, 777220526035, 4336186086677] "" "Class ", 1533, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, %1], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, %1], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, %1], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, %1], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, %1], [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, %1], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2282, 12804, 76972, 492180, 3328625, 23701857, 177033081, 1382667294, 11261754716, 95434783773, 839708029028, 7657339936483, 72250928537345, 704336610785163] "" "Class ", 1534, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 2]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 2]}], [[3, 1, 2], {1}, {[0, 0, 0, 2]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 413, 2018, 10495, 57598, 331471, 1990317, 12419366, 80268244, 535868221, 3686582309, 26083511772, 189462207560, 1410667948623, 10751784936281, 83784160593972] "" "Class ", 1535, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1, 3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 400, 1908, 9694, 52186, 296530, 1773274, 11134040, 73254036, 504126054, 3622927138, 27146374526, 211757037078, 1717108955676, 14453383635852, 126109991934786] "" "Class ", 1536, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 1, 4], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {2}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 385, 1752, 8298, 40595, 203978, 1048207, 5490610, 29238928, 157960904, 864237742, 4781782561, 26723794265, 150701348257, 856782207417, 4907203366563] "" "Class ", 1537, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 488, 2736, 16818, 111896, 798688, 6071398, 48867976, 414474913, 3689334856, 34345927571, 333413776191, 3366219876529, 35266073090707, 382599618643394, 4290581647848623] "" "Class ", 1538, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [ [3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622] "" "Class ", 1539, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 1, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 1, 5, 2, 4], {2, 3}, {}], [[3, 2, 4, 1, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 1, 5, 2, 3], {1, 2, 3}, {}], [[4, 1, 5, 3, 2], {1}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 2, 5, 3, 1], {1}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 474, 2596, 15492, 99552, 682524, 4956182, 37898550, 303705340, 2540424146, 22105959742, 199527230068, 1863336925076, 17964786212450, 178464684246688, 1823621865741740] "" "Class ", 1540, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622] "" "Class ", 1541, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "Class ", 1542, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 1543, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "Class ", 1544, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 1545, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2699, 16702, 112621, 819763, 6393582, 53105303, 467368097, 4339457377, 42350609478, 433048456814, 4626398053439, 51510799911179, 596403235285935, 7166474544795229] "" "Class ", 1546, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 443, 2341, 13550, 85048, 574340, 4146278, 31826634, 258575382, 2214872372, 19934175317, 187949348795, 1851531438224, 19012905933100, 203084969259619, 2252129386525353] "" "Class ", 1547, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1548, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 429, 2200, 12270, 73763, 474538, 3247596, 23526211, 179642767, 1440669569, 12096341063, 106044121595, 968299711767, 9189409381880, 90465228236738, 922224531034287] "" "Class ", 1549, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1550, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1551, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1552, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1553, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2697, 16748, 113551, 832446, 6547885, 54912120, 488379495, 4585868058, 45288904189, 468837417245, 5072805216480, 57220826125390, 671350003584763, 8176104236709609] "" "Class ", 1554, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2580, 15676, 103798, 742269, 5691027, 46500543, 402868772, 3684954920, 35452500425, 357601390221, 3770955185703, 41467428448721, 474448115770721, 5636622667144835] "" "Class ", 1555, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1556, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1557, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1558, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1559, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1560, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1561, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2789, 17429, 118596, 870423, 6841139, 57231790, 507074076, 4737913434, 46515354251, 478321851393, 5137480348868, 57493286083112, 668911771315175, 8075167553148301] "" "Class ", 1562, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2488, 14835, 96077, 670029, 4996318, 39613511, 332369303, 2939169802, 27298914917, 265502947143, 2696738709575, 28538221515477, 313990072995030, 3584928084670801] "" "Class ", 1563, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 1564, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 1565, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 1566, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 1567, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 1568, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 1569, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 488, 2753, 17088, 115445, 840415, 6544300, 54172781, 474332648, 4374418421, 42337552450, 428686257392, 4528743021715, 49796189592027, 568680354689801, 6732325377909287] "" "Class ", 1570, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {[1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2364, 13432, 81715, 528213, 3606274, 25878693, 194408222, 1523720697, 12423912094, 105120481604, 920964886644, 8338512509290, 77889692555051, 749465249728372] "" "Class ", 1571, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1572, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1573, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1574, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1575, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1576, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1577, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2832, 17947, 124112, 927350, 7427885, 63373657, 572906005, 5463369687, 54751267598, 574727427044, 6301188098262, 71975135138339, 854617320009597, 10527439981057879] "" "Class ", 1578, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2481, 14821, 96337, 675381, 5070524, 40527908, 343172725, 3065539091, 28785027565, 283220738060, 2911927285671, 31208185017339, 347887706583962, 4025679868968173] "" "Class ", 1579, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1580, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1581, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1582, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2184, 12096, 72104, 459440, 3111616, 22292592, 168263312, 1333377904, 11059335280, 95753379216, 863373139824, 8089902823120, 78625465178608, 791248858589264] "" "Class ", 1583, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1584, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1585, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2581, 15599, 102301, 721789, 5439815, 43544672, 368456163, 3282386850, 30679108637, 299944373424, 3059425511081, 32480959908322, 358184005403761, 4095086613385369] "" "Class ", 1586, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [ [2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2154, 11660, 67097, 407560, 2598902, 17321748, 120237561, 866635889, 6469666072, 49915147781, 397254838845, 3255924359506, 27441793746908, 237529458553869] "" "Class ", 1587, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 1588, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 1589, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 1590, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 1591, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 1592, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 1593, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1594, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2285, 12834, 77199, 493218, 3326369, 23557940, 174471166, 1346370314, 10793270339, 89648976326, 769764394167, 6818965854160, 62210186733939, 583579855363878] "" "Class ", 1595, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1596, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1597, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1598, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1599, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1600, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 0]]} "Class ", 1601, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2575, 15615, 103059, 733587, 5590616, 45340292, 389347915, 3525140611, 33529027151, 333965339186, 3473913509802, 37645714836699, 424081517203937, 4956518328046508] "" "Class ", 1602, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2154, 11660, 67097, 407560, 2598902, 17321748, 120237561, 866635889, 6469666072, 49915147781, 397254838845, 3255924359506, 27441793746908, 237529458553869] "" "Class ", 1603, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1604, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1605, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1606, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1607, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1608, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1609, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2659, 16554, 112637, 829187, 6551693, 55201231, 493277116, 4653751080, 46174025079, 480194243779, 5219018450974, 59128073154445, 696688079652715, 8519921541074856] "" "Class ", 1610, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2222, 12554, 76877, 506562, 3569690, 26764369, 212562941, 1781351574, 15699291537, 145072659365, 1401894448566, 14133149308115, 148329849502286, 1617499701611444] "" "Class ", 1611, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2220, 12536, 76776, 506326, 3573608, 26851528, 213816756, 1797240686, 15891147852, 147352644760, 1428997643936, 14458348763350, 152289219931872, 1666573500982280] "" "Class ", 1612, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 400, 1913, 9785, 53240, 306595, 1860393, 11849077, 78952813, 548793818, 3969349924, 29808142527, 231952008171, 1866983035869, 15519172835770, 133031501665782] "" "Class ", 1613, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "Class ", 1614, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 1615, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[2, 3, 1, 4], {2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 398, 1882, 9470, 50538, 285166, 1696314, 10607582, 69546634, 476889422, 3412389210, 25427131966, 196928209578, 1582458775214, 13172695692922, 113421127349918] "" "Class ", 1616, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 1617, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2178, 12117, 72960, 472436, 3271774, 24114737, 188360654, 1553397639, 13480803184, 122744594676, 1169473929947, 11631694689607, 120509604740557, 1298000860296892] "" "Class ", 1618, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[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, 6, 22, 90, 396, 1861, 9318, 49541, 278537, 1649502, 10253098, 66690223, 452688142, 3199018316, 23484112001, 178741256163, 1408003797375, 11460856095825, 96256917750525] "" "Class ", 1619, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1620, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1621, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2767, 17485, 120691, 900630, 7207402, 61454003, 555309471, 5293977503, 53043141668, 556728135389, 6103436855126, 69714629882260, 827783563891539, 10197235926168322] "" "Class ", 1622, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2485, 14905, 97519, 689724, 5234468, 42364798, 363763798, 3299096714, 31483114036, 315085797775, 3297513475087, 35994435213403, 408867017132639, 4823220043393807] "" "Class ", 1623, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 1624, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 1625, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {}, {}], [[4, 1, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 2, 3], {2, 3}, {}], [[5, 1, 4, 3, 2], {4}, {}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 2, 4, 3, 1], {4}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2470, 14740, 95884, 674026, 5083754, 40895126, 349088978, 3148410448, 29888457928, 297677109730, 3101417852134, 33715778398130, 381565302991002, 4486147856471508] "" "Class ", 1626, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2184, 12096, 72104, 459440, 3111616, 22292592, 168263312, 1333377904, 11059335280, 95753379216, 863373139824, 8089902823120, 78625465178608, 791248858589264] "" "Class ", 1627, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 1628, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {5}, {[0, 0, 0, 0, 1, 0]}], [[2, 1, 5, 3, 4], {5}, {[0, 0, 0, 0, 1, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 2, 4], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 392, 1772, 8197, 38493, 182634, 872922, 4195041, 20244585, 98018532, 475837452, 2315035819, 11283740331, 55084255670, 269270598506, 1317843922156] "" "Class ", 1629, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2601, 15842, 104975, 750046, 5737360, 46710742, 402785886, 3663302390, 35014651484, 350625460572, 3668222824928, 39996723995010, 453525063919592, 5337457953769932] "" "Class ", 1630, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2224, 12622, 77980, 520610, 3731513, 28551364, 232051722, 1994719058, 18066558394, 171838932102, 1711365267293, 17799288606948, 192879111809651, 2173085790299502] "" "Class ", 1631, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 1632, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 1633, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2301, 13020, 79024, 510216, 3481922, 24989790, 187849377, 1473966713, 12037868694, 102075913909, 896757240290, 8146722096504, 76404388937871, 738634149462483] "" "Class ", 1634, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 1, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1844, 9015, 46074, 245583, 1363285, 7874474, 47291208, 295082392, 1911421628, 12841667647, 89392093304, 644054083218, 4797444285053, 36904529600896] "" "Class ", 1635, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 1636, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 1637, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 1638, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2152, 11729, 68355, 422784, 2758310, 18885664, 135128242, 1006765880, 7786708488, 62356006287, 515830491203, 4399127111486, 38608663873516, 348156150091432] "" "Class ", 1639, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 1640, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 1641, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 1642, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1844, 9015, 46023, 244382, 1345306, 7656798, 44949634, 271631086, 1686691262, 10745242177, 70132163377, 468380781890, 3197241967014, 22284705750226] "" "Class ", 1643, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 1644, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 1645, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2}, {}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2}, {}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2619, 16083, 107782, 780655, 6064144, 50205871, 440695059, 4083174128, 39782045166, 406236397280, 4335356795912, 48230734540176, 558080584352148, 6702978502287345] "" "Class ", 1646, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 430, 2224, 12622, 77980, 520610, 3731513, 28551364, 232051722, 1994719058, 18066558394, 171838932102, 1711365267293, 17799288606948, 192879111809651, 2173085790299502] "" "Class ", 1647, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1648, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1649, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1650, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}] , [[3, 4, 1, 2], {1}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[4, 1, 3, 2], {}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {[1, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 397, 1866, 9301, 49010, 272220, 1589321, 9727389, 62257506, 415720965, 2890113545, 20878387368, 156453620568, 1214178341803, 9744202659930, 80758242806675] "" "Class ", 1651, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1652, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1653, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]} "Class ", 1654, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 377, 1635, 7202, 32184, 146072, 674220, 3167368, 15148824, 73755332, 365417065, 1841438541, 9433372082, 49099875679, 259515603561, 1392164589780] "" "Class ", 1655, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 1, 4], {3}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {}], [[2, 4, 3, 1, 5], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {4}, {}], [[3, 2, 4, 1, 5], {3, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 1, 4], {1, 2}, {}], [[3, 4, 2, 1, 5], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 1, 3, 2, 5], {2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 2, 3, 1, 5], {2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 2, 5, 1, 3], {1, 2}, {}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {4}, {}], [[4, 5, 2, 1, 3], {1, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {}], [[5, 1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {4}, {}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {4}, {}], [[5, 3, 4, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 395, 1833, 8945, 45783, 245304, 1373496, 8023112, 48813656, 308842937, 2028970755, 13820752715, 97479846093, 710997401630, 5356319647258, 41630966375594] "" "Class ", 1656, " is:" {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 358, 1435, 5603, 21269, 78661, 284460, 1009740, 3530942, 12202084, 41782376, 142073803, 480570394, 1619282610, 5440985564, 18246471724] "" "Class ", 1657, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {2}, {}], [[1, 5, 3, 2, 4], {2, 3}, {}], [[1, 5, 4, 2, 3], {2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 534, 3271, 22657, 174813, 1486950, 13822059, 139377627, 1515246951, 17665904946, 219862324692, 2909233005408, 40782416999256, 603752675401512, 9412509117886155, 154135523737447983] "" "Class ", 1658, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2883, 18798, 135969, 1081562, 9392385, 88489090, 899556302, 9819875902, 114621705426, 1425109669168, 18808403939587, 262676686038748, 3871011951733185, 60039488908269026] "" "Class ", 1659, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1660, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1661, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2922, 19181, 139399, 1110463, 9618591, 89981338, 903950789, 9704239308, 110854741506, 1342462245935, 17177960947712, 231571784628075, 3280186932258714, 48705386018405462] "" "Class ", 1662, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2553, 15292, 99233, 691632, 5142487, 40565057, 337925699, 2961412681, 27210841334, 261394120931, 2618533655490, 27293009418886, 295394053393594, 3313771903807877] "" "Class ", 1663, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1664, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1665, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {2, 3}, {}], [[1, 4, 2, 3, 5], {2}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {2}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2949, 19447, 141942, 1135177, 9865267, 92533575, 931429245, 10012080952, 114438326196, 1385709713740, 17717288724841, 238492559146173, 3371058054995259, 49916669180137771] "" "Class ", 1666, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2639, 16341, 110749, 813960, 6439076, 54492899, 490817915, 4684484078, 47197409433, 500324125420, 5564083466727, 64746800342710, 786534730182291, 9953724256858268] "" "Class ", 1667, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 1668, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 1669, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2532, 15420, 102620, 739512, 5729192, 47429896, 417429800, 3888426512, 38192416048, 394239339792, 4264424937488, 48212317486112, 568395755184224, 6973300915138656] "" "Class ", 1670, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2317, 13202, 80896, 528842, 3665479, 26801239, 205870087, 1655504471, 13895499376, 121424960137, 1102187017573, 10371787758966, 101003056696585, 1016267738355791] "" "Class ", 1671, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 1672, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 1673, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {2}, {}], [[1, 5, 3, 2, 4], {2, 3}, {}], [[1, 5, 4, 2, 3], {2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3193, 21951, 168208, 1421251, 13127135, 131567085, 1422027409, 16487030976, 204100275732, 2686915476466, 37481882206929, 552286385027683, 8571279585771979, 139749690441102521] "" "Class ", 1674, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2883, 18798, 135969, 1081562, 9392385, 88489090, 899556302, 9819875902, 114621705426, 1425109669168, 18808403939587, 262676686038748, 3871011951733185, 60039488908269026] "" "Class ", 1675, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 1676, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 1677, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2790, 17874, 126260, 974056, 8143110, 73294136, 706384540, 7255499970, 79100654118, 912076499426, 11087998533588, 141718997445238, 1899610606246638, 26642721217362962] "" "Class ", 1678, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2405, 13854, 85662, 563933, 3927979, 28803812, 221467059, 1779442990, 14898367193, 129661903988, 1170532335872, 10940605161424, 105697978841150, 1053938072270265] "" "Class ", 1679, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 1680, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 1681, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3131, 21418, 163434, 1375629, 12659367, 126447894, 1362344982, 15747572037, 194391942423, 2552209522158, 35511497125998, 521974868042769, 8081953240629939, 131477250755979894] "" "Class ", 1682, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 476, 2717, 17414, 124035, 973530, 8358619, 78006890, 786875468, 8536552470, 99155943686, 1228196083904, 16164200188005, 225296300050544, 3315705356679271, 51386122957665042] "" "Class ", 1683, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 1684, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 1685, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2948, 19468, 142536, 1145054, 10011760, 94627066, 961201586, 10441276956, 120769417766, 1481764208064, 19220564264696, 262797966217640, 3777325930373024, 56938393801915768] "" "Class ", 1686, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2492, 14898, 96740, 676334, 5054712, 40148126, 337247152, 2983672994, 27703433136, 269127649450, 2728059162792, 28786214210198, 315521276267616, 3585582242680438] "" "Class ", 1687, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 1688, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 1689, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 5, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2311, 13115, 79996, 520632, 3595778, 26241820, 201670013, 1627458658, 13758212346, 121589635246, 1121278361435, 10771754517244, 107632981323836, 1117027381168560] "" "Class ", 1690, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2109, 11178, 62565, 367396, 2252254, 14357825, 94882895, 648334074, 4570773596, 33187256140, 247779974828, 1899700454599, 14938593967493, 120359092984631] "" "Class ", 1691, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 408, 1935, 9569, 48872, 256076, 1369956, 7456119, 41170959, 230146330, 1300184577, 7412919029, 42605043898, 246609069238, 1436444028540, 8414117303283] "" "Class ", 1692, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3098, 21112, 160524, 1347036, 12364608, 123229530, 1325094402, 15290877840, 188469057024, 2471107755330, 34341400892898, 504224158501614, 7799372715477558, 126765665821947282] "" "Class ", 1693, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2629, 16310, 111403, 831419, 6737013, 58946329, 554217353, 5575083865, 59768512095, 680468587247, 8201004078431, 104324257759604, 1397049157503918, 19646943969384120] "" "Class ", 1694, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "Class ", 1695, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 1696, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {2, 3}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2808, 18282, 132672, 1063122, 9330144, 89045046, 918468480, 10183816854, 120807999360, 1526893903818, 20485349775360, 290780492531490, 4353992234104320, 68588265490962390] "" "Class ", 1697, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 1698, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2575, 15588, 102644, 728682, 5537303, 44777698, 383435561, 3462387194, 32851121338, 326481019906, 3389270607895, 36663946764588, 412396688839795, 4813809477276832] "" "Class ", 1699, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 1700, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {2, 3}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2949, 19596, 144827, 1178331, 10465832, 100759041, 1045128895, 11619121523, 137826004442, 1737482246469, 23196218412290, 326937350465415, 4851163702703134, 75590060269036476] "" "Class ", 1701, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2513, 15185, 100106, 713691, 5463452, 44642158, 387402847, 3555150289, 34373264719, 349015028525, 3710968905390, 41214328824192, 477025139204996, 5742217982145530] "" "Class ", 1702, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1703, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1704, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 463, 2582, 16089, 110901, 838040, 6890249, 61246888, 585345457, 5985946426, 65225717998, 754487804704, 9234032629968, 119218907953002, 1619383069843465, 23086109369101302] "" "Class ", 1705, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 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}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 415, 2060, 10999, 62597, 377322, 2397369, 15992320, 111645938, 813535959, 6173537507, 48692467316, 398479195081, 3378243122525, 29628251389083, 268467081983142] "" "Class ", 1706, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1707, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1708, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {2, 3}, {}], [[1, 3, 2, 4, 5], {2}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {2}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 495, 2880, 18808, 136296, 1084864, 9406933, 88249182, 890526549, 9617949487, 110693309712, 1352371511869, 17479572392476, 238292549351217, 3417077789170308, 51416075488499296] "" "Class ", 1709, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2, 3}, {[1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 479, 2690, 16733, 114093, 844762, 6742934, 57661150, 525517716, 5081734327, 51937480358, 559140863061, 6321729764653, 74863396919238, 926378174836366, 11952554433905482] "" "Class ", 1710, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1711, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1712, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 451, 2389, 13801, 86193, 577943, 4136818, 31455797, 253021874, 2145052624, 19104276004, 178232505019, 1737378518104, 17654573427981, 186629000727935, 2048565905766453] "" "Class ", 1713, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2219, 12102, 70130, 429281, 2763772, 18653383, 131634728, 969167956, 7430790052, 59232792856, 490150486601, 4204674760844, 37342434299922, 342926195825273] "" "Class ", 1714, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1715, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1716, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {2, 3}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2977, 19877, 147503, 1204166, 10722711, 103409061, 1073580976, 11937002898, 141513236790, 1781709757402, 23741625311564, 333794056933284, 4937894548971730, 76668850387135437] "" "Class ", 1717, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2513, 15185, 100106, 713691, 5463452, 44642158, 387402847, 3555150289, 34373264719, 349015028525, 3710968905390, 41214328824192, 477025139204996, 5742217982145530] "" "Class ", 1718, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 1719, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 1720, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 462, 2570, 15946, 109074, 814904, 6599576, 57570120, 538030322, 5361989734, 56754091670, 635734828586, 7512670156760, 93396645162166, 1218401577683002, 16641081454962728] "" "Class ", 1721, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 1722, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 1723, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 1724, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {2}, {}], [[1, 5, 3, 2, 4], {2, 3}, {}], [[1, 5, 4, 2, 3], {2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3221, 22381, 173658, 1487003, 13925017, 141529665, 1551351071, 18239779428, 228947736462, 3055482005230, 43199873944925, 644991193949199, 10140302210593381, 167438929613233613] "" "Class ", 1725, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2808, 18282, 132672, 1063122, 9330144, 89045046, 918468480, 10183816854, 120807999360, 1526893903818, 20485349775360, 290780492531490, 4353992234104320, 68588265490962390] "" "Class ", 1726, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1727, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1728, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 483, 2767, 17797, 126980, 995005, 8493682, 78446158, 779342467, 8286907959, 93901130659, 1129534672406, 14374917946178, 192962925052487, 2724741717322779, 40373364062370107] "" "Class ", 1729, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 452, 2400, 13908, 87187, 587049, 4220667, 32241252, 260557152, 2219359580, 19858783953, 186125140793, 1822414241551, 18597577104952, 197382919869624, 2174550349707782] "" "Class ", 1730, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1731, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1732, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 5, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 521, 3144, 21363, 161410, 1341534, 12161075, 119379641, 1261429956, 14273323111, 172175801902, 2205473970113, 29895915230193, 427528313253376, 6432261043082454, 101561579706855648] "" "Class ", 1733, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 483, 2741, 17300, 120131, 909783, 7459938, 65824137, 621750227, 6258425735, 66868008858, 755726580558, 9006619098000, 112878067621034, 1483981657723019, 20419376809575296] "" "Class ", 1734, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1735, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1736, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2714, 16975, 116359, 866069, 6947632, 59696167, 546517928, 5307107262, 54452573559, 588314550153, 6673138917336, 79254520375991, 983234954563299, 12714509542524793] "" "Class ", 1737, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 451, 2373, 13485, 81855, 526458, 3565412, 25301642, 187391383, 1443710460, 11538140460, 95431086230, 815184064105, 7178923775487, 65075664329219, 606354883752396] "" "Class ", 1738, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1739, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1740, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3143, 21615, 165803, 1403042, 12981618, 130361057, 1411901219, 16404556474, 203520006966, 2685124582110, 37538504338044, 554317168648328, 8621202697991264, 140860299502726544] "" "Class ", 1741, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2651, 16606, 114789, 868055, 7129409, 63206311, 601716445, 6123097197, 66338266720, 762490209174, 9268477389165, 118809452058064, 1601931634240347, 22665762491457133] "" "Class ", 1742, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 1743, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 1744, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 489, 2851, 18752, 137471, 1111981, 9841688, 94633366, 982596494, 10958947274, 130682536700, 1659398053692, 22356066232960, 318527455185033, 4785667016919455, 75620921662053474] "" "Class ", 1745, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 1746, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 1747, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 1748, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3}, {}], [[1, 5, 4, 2, 3], {2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2992, 20164, 151645, 1258649, 11424655, 112557315, 1196031853, 13633283215, 165926869861, 2147427222046, 29447122921988, 426483031010591, 6505093266600066, 104227184482210692] "" "Class ", 1749, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 475, 2703, 17226, 121659, 943474, 7972371, 72922400, 717930494, 7569996246, 85115508040, 1016592183779, 12853450841176, 171511904656527, 2408635155261155, 35511260750350867] "" "Class ", 1750, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1751, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1752, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2529, 15542, 105616, 787274, 6391735, 56167353, 531247881, 5381766311, 58141244572, 667279852625, 8107986246883, 103985513905130, 1403765037588360, 19897531679136124] "" "Class ", 1753, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 431, 2223, 12463, 75335, 487709, 3363034, 24591809, 189971705, 1545176693, 13194164018, 117965848970, 1101706683287, 10724323020090, 108594655214609, 1141808673573613] "" "Class ", 1754, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1755, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[3, 4, 2, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 0, 1]]} "Class ", 1756, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2, 3}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2946, 19669, 146452, 1202379, 10787924, 105001935, 1101818855, 12398003830, 148906051635, 1901235907101, 25714238536020, 367238589586091, 5522400005902559, 87217441481635395] "" "Class ", 1757, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2509, 15303, 103085, 761517, 6128940, 53418437, 501445642, 5044971986, 54163180271, 618125227580, 7472618974551, 95399483269419, 1282574863840469, 18112788996519094] "" "Class ", 1758, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1759, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1760, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2423, 14236, 91006, 627754, 4641085, 36572018, 305718979, 2700010379, 25103606101, 244952942040, 2501552364124, 26671787090540, 296248292674574, 3421058808633628] "" "Class ", 1761, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 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, 3, 4, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1953, 9777, 50910, 274509, 1529090, 8787876, 52069365, 317888022, 1998490257, 12929251072, 86011499157, 587882883480, 4124787015205, 29683411358648] "" "Class ", 1762, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1763, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1764, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 2989, 19999, 148617, 1213748, 10802424, 104035558, 1077753856, 11948444668, 141134034411, 1769279398808, 23459503670082, 328002326835770, 4822662516201828, 74384459488062646] "" "Class ", 1765, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2482, 14838, 96557, 678006, 5100953, 40878634, 347242195, 3113427111, 29359227701, 290256540098, 3000184498875, 32342721908895, 362841259090965, 4227797242692957] "" "Class ", 1766, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 1, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2530, 15390, 102324, 736940, 5707524, 47249192, 415958350, 3877180502, 38120023020, 394030262902, 4269566525436, 48372158978220, 571693060402942, 7033718512486882] "" "Class ", 1767, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2163, 11807, 68762, 423968, 2751126, 18701205, 132682525, 979594216, 7507423035, 59598777695, 489218191722, 4145753381285, 36218991018312, 325808161038279] "" "Class ", 1768, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 1, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 461, 2551, 15703, 106349, 785543, 6283016, 54087684, 498555676, 4898576693, 51105475269, 564165630693, 6569828888219, 80485168085734, 1034705080988440, 13927790585657039] "" "Class ", 1769, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 1770, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2183, 12060, 71452, 450491, 3004132, 21085220, 155127196, 1192181291, 9542179898, 79338132460, 683697057547, 6094335010987, 56091753460251, 532220250850278] "" "Class ", 1771, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 1772, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1773, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 406, 1916, 9492, 49280, 268577, 1540441, 9308253, 59204192, 395564996, 2769849558, 20279942512, 154910349863, 1231923388312, 10179792290292, 87253681392316] "" "Class ", 1774, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 390, 1747, 8002, 37306, 176686, 849048, 4133530, 20350568, 101133154, 506484394, 2552837913, 12936521933, 65856603714, 336584116681, 1726161764785] "" "Class ", 1775, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 5, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3050, 20486, 152749, 1251433, 11169340, 107841999, 1119723999, 12439002990, 147197282282, 1848324668094, 24543849876210, 343619543685001, 5058314214450244, 78102563835362885] "" "Class ", 1776, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2698, 16819, 115093, 857522, 6908818, 59841528, 554461283, 5471776372, 57296259990, 634467944607, 7407687549035, 90945912098105, 1171285720775479, 15789578779418468] "" "Class ", 1777, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 1778, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 1779, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2729, 17143, 118077, 883278, 7121736, 61501751, 565854679, 5521720179, 56924818106, 617884691387, 7040273924329, 83983150500170, 1046362875882616, 13587236077373948] "" "Class ", 1780, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 451, 2373, 13485, 81855, 526458, 3565412, 25301642, 187391383, 1443710460, 11538140460, 95431086230, 815184064105, 7178923775487, 65075664329219, 606354883752396] "" "Class ", 1781, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 1782, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 1783, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3140, 21569, 165255, 1396662, 12906180, 129437302, 1400089581, 16246481995, 201303881283, 2652580210970, 37038235366721, 546275657067254, 8486193819578268, 138495872143854217] "" "Class ", 1784, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2682, 16939, 117932, 896386, 7381363, 65431226, 620997559, 6281045796, 67430934344, 765660878265, 9166571360964, 115388311449126, 1523410480934544, 21047181784115533] "" "Class ", 1785, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 1786, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 1787, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 489, 2851, 18752, 137471, 1111981, 9841688, 94633366, 982596494, 10958947274, 130682536700, 1659398053692, 22356066232960, 318527455185033, 4785667016919455, 75620921662053474] "" "Class ", 1788, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2247, 12382, 72577, 449153, 2917555, 19797846, 139805897, 1024188482, 7763409301, 60756376446, 489984198619, 4065489869105, 34654446671122, 303085403587265] "" "Class ", 1789, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 1790, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 1791, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 3001, 20224, 151836, 1256019, 11347594, 111153494, 1173198643, 13272545846, 160207439060, 2055028174175, 27914217181912, 400259645648314, 6041519606733698, 95750167505720833] "" "Class ", 1792, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 461, 2561, 15912, 109515, 827720, 6818434, 60827746, 584377304, 6016222106, 66086632986, 771599923179, 9542667828032, 124626559007261, 1713997191650467, 24761552310930542] "" "Class ", 1793, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 1794, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 1795, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {3}, {}], [[1, 5, 4, 2, 3], {3}, {}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 3, 4, 1], {1, 3}, {}], [[2, 5, 4, 3, 1], {1, 3}, {}], [[4, 1, 2, 3, 5], {1, 3}, {}], [[4, 1, 3, 2, 5], {1, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {3}, {}], [[5, 1, 4, 2, 3], {3}, {}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 3, 4, 1], {2, 3}, {}], [[5, 2, 4, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 462, 2566, 15900, 108832, 815664, 6645202, 58490086, 553238442, 5597348206, 60327943594, 690150398922, 8353133551314, 106652090551184, 1432712156053130, 20201284445679346] "" "Class ", 1796, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 431, 2223, 12463, 75335, 487709, 3363034, 24591809, 189971705, 1545176693, 13194164018, 117965848970, 1101706683287, 10724323020090, 108594655214609, 1141808673573613] "" "Class ", 1797, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 1798, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 1799, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {2, 3}, {}], [[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, 6, 22, 97, 500, 2955, 19727, 146688, 1201385, 10744586, 104180961, 1088400811, 12187095652, 145594627309, 1848375605506, 24848688609529, 352634037468286, 5267858029508616, 82629543777368029] "" "Class ", 1800, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2507, 15251, 102185, 748156, 5943484, 50913224, 467758265, 4587597712, 47834964987, 528362782406, 6162397160644, 75674412955426, 975903670629074, 13185833783646834] "" "Class ", 1801, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1802, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1803, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[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]}], [[4, 1, 2, 3, 5], {1, 3}, {}], [[4, 1, 3, 2, 5], {1, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {3}, {}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2423, 14236, 91006, 627754, 4641085, 36572018, 305718979, 2700010379, 25103606101, 244952942040, 2501552364124, 26671787090540, 296248292674574, 3421058808633628] "" "Class ", 1804, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [1, 5, 2, 3, 4], {1}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 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]}], [[4, 1, 2, 3, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [5, 1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2095, 11048, 61562, 360443, 2207813, 14097952, 93572034, 643963836, 4585495380, 33722851417, 255725346191, 1996683528576, 16031292911487, 132203568530189] "" "Class ", 1805, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1806, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]} "Class ", 1807, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [2, 5, 3, 4, 1], {1, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {1, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 4, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 417, 2093, 11373, 66251, 410573, 2690921, 18566032, 134344777, 1016351820, 8017228385, 65788991745, 560464124060, 4947945576812, 45194230122244, 426469907244417] "" "Class ", 1808, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {2, 3}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {2, 3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {2, 3, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [4, 5, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 431, 2232, 12598, 76585, 496988, 3419623, 24814720, 189062775, 1506719953, 12519639878, 108163463404, 969287023443, 8990597084422, 86153978324553, 851504451185769] "" "Class ", 1809, " is:" {{[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 1810, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 3, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 103, 516, 2820, 16536, 102824, 672174, 4589163, 32555137, 238979864, 1809313425, 14089122384, 112583004368, 921369656426, 7709778052266, 65867226668123, 573811218358675] "" "Class ", 1811, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 487, 2708, 16403, 106906, 743108, 5471975, 42458490, 345653861, 2941890212, 26098505507, 240709646014, 2302996088760, 22812199689949, 233541984252754, 2467268936862200] "" "Class ", 1812, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2360, 13344, 80446, 512842, 3435592, 24066964, 175600380, 1330159772, 10432248488, 84517737112, 705917761402, 6068054295922, 53601615376196, 485912800856588] "" "Class ", 1813, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1814, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1815, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2424, 14090, 88184, 589300, 4177440, 31248612, 245599126, 2020850594, 17354981328, 155150221730, 1440528577804, 13862922749170, 138029364200948, 1419625997273008] "" "Class ", 1816, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2108, 11148, 62096, 361680, 2190720, 13739736, 88919968, 592140320, 4047967744, 28351717168, 203104858976, 1486035040064, 11090626172448, 84337068089184] "" "Class ", 1817, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1818, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1819, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2610, 15577, 99970, 683939, 4955116, 37818207, 302774336, 2533884609, 22101543490, 200414926198, 1885205233710, 18360077996305, 184815746444603, 1919957918868731] "" "Class ", 1820, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2411, 13963, 87042, 579259, 4088943, 30457287, 238374743, 1953283669, 16706473009, 148757363759, 1375787882351, 13189453993725, 130835235093995, 1340746108292891] "" "Class ", 1821, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 1822, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 1823, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2298, 12967, 78421, 504442, 3430805, 24554151, 184210671, 1443988074, 11794579296, 100149247378, 882198744660, 8047314804252, 75892620322949, 738892803484753] "" "Class ", 1824, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2146, 11624, 67146, 411142, 2656052, 18035178, 128318314, 954086192, 7396278762, 59659032142, 499778527628, 4341025729290, 39035256389026, 362878164902216] "" "Class ", 1825, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 1826, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 1827, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2610, 15577, 99970, 683939, 4955116, 37818207, 302774336, 2533884609, 22101543490, 200414926198, 1885205233710, 18360077996305, 184815746444603, 1919957918868731] "" "Class ", 1828, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2360, 13344, 80446, 512842, 3435592, 24066964, 175600380, 1330159772, 10432248488, 84517737112, 705917761402, 6068054295922, 53601615376196, 485912800856588] "" "Class ", 1829, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 1830, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 1831, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2405, 13854, 85662, 563933, 3927979, 28803812, 221467059, 1779442990, 14898367193, 129661903988, 1170532335872, 10940605161424, 105697978841150, 1053938072270265] "" "Class ", 1832, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2108, 11148, 62096, 361680, 2190720, 13739736, 88919968, 592140320, 4047967744, 28351717168, 203104858976, 1486035040064, 11090626172448, 84337068089184] "" "Class ", 1833, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 1834, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 1835, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2496, 14562, 91050, 604814, 4240166, 31208644, 240134025, 1924863442, 16026397712, 138252718208, 1233031405134, 11347949817244, 107592219913672, 1049354101559658] "" "Class ", 1836, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2141, 11529, 65902, 397098, 2508534, 16541078, 113441070, 806750068, 5934297612, 45052450361, 352346487861, 2834068701373, 23410500306299, 198340840318963] "" "Class ", 1837, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 1838, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 1839, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 451, 2373, 13488, 81903, 526982, 3570181, 25339653, 187654481, 1445108991, 11539669456, 95320338266, 812771130804, 7140810231834, 64539130788912, 599201066502367] "" "Class ", 1840, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 412, 2002, 10306, 55709, 314146, 1838880, 11130244, 69443396, 445473992, 2931927554, 19762407890, 136210309369, 958694809278, 6882401216326, 50342758287742] "" "Class ", 1841, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 1842, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 1843, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 397, 1852, 9025, 45558, 236792, 1261489, 6864183, 38042943, 214270206, 1224189966, 7083799809, 41462017847, 245200464626, 1463748537739, 8813103773183] "" "Class ", 1844, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {3}, {[0, 0, 0, 1]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 368, 1584, 6968, 31192, 141656, 651136, 3023840, 14166496, 66876096, 317809216, 1519163456, 7299577216, 35237444736, 170812433536, 831127053696] "" "Class ", 1845, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 461, 2452, 14075, 86231, 559355, 3818329, 27298683, 203616624, 1579428120, 12706707096, 105782465139, 909445902630, 8060565134124, 73537804244561, 689630571398761] "" "Class ", 1846, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 1847, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2325, 12927, 76131, 470974, 3041327, 20399679, 141570476, 1013267555, 7459852512, 56367414521, 436314387474, 3454152342144, 27928267456459, 230341992399658] "" "Class ", 1848, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 1849, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2219, 12091, 69881, 425523, 2715996, 18096765, 125449688, 902169556, 6713973463, 51594410824, 408628187340, 3329833818149, 27876129669200, 239428020642638] "" "Class ", 1850, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 1851, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1, 3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2076, 10798, 58816, 333224, 1953860, 11811698, 73400220, 467746132, 3050717100, 20331354242, 138263235764, 958323863156, 6763014016044, 48551505630068] "" "Class ", 1852, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {3, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 1853, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 449, 2346, 13254, 80181, 515586, 3504813, 25075052, 188120649, 1475395938, 12064478116, 102620612258, 906158522928, 8291472297419, 78489476264883, 767547057991948] "" "Class ", 1854, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1983, 10220, 55793, 321062, 1940751, 12292170, 81406992, 562697944, 4052903290, 30373630090, 236520131207, 1911207102444, 16005331137509, 138741975127776] "" "Class ", 1855, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1856, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 395, 1829, 8863, 44719, 234020, 1266160, 7064778, 40571250, 239425846, 1450167918, 9005796164, 57294989776, 373155030530, 2486380954232, 16939868491280] "" "Class ", 1857, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1858, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1859, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1860, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1861, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, %1], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2}, %1], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2}, %1], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 2, 3, 4], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 461, 2466, 14333, 89631, 598224, 4234574, 31627923, 248209307, 2039452009, 17492155296, 156196438370, 1448782424757, 13930352449184, 138601143785988, 1424677999726321] "" "Class ", 1862, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [1, 5, 2, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 449, 2357, 13417, 82062, 535275, 3701610, 27006430, 207036350, 1662022743, 13930186177, 121588457836, 1102718317200, 10370655034905, 100958345323789, 1015723790368167] "" "Class ", 1863, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1864, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1865, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1866, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1867, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1868, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1869, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 477, 2618, 15629, 100344, 686829, 4978818, 38023821, 304644205, 2551592375, 22275373810, 202177869406, 1903631408403, 18558192089129, 187003795098049, 1944752705159676] "" "Class ", 1870, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2299, 12991, 78771, 508593, 3475672, 25020235, 188986044, 1492898284, 12299240118, 105420298180, 938101649617, 8650534112248, 82523490609012, 813205423864142] "" "Class ", 1871, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 1872, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 1873, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 1874, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 1875, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 1876, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 1877, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 472, 2558, 15001, 94261, 629452, 4440662, 32931442, 255701718, 2071918836, 17471616284, 152963662675, 1387564562080, 13018153881340, 126121288906202, 1259953199966113] "" "Class ", 1878, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2218, 12069, 69566, 421790, 2675999, 17692289, 121494335, 864204396, 6352792944, 48166092610, 376009162737, 3017706190471, 24865179607803, 210096204695519] "" "Class ", 1879, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1880, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1881, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1882, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1883, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1884, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1885, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 477, 2631, 15824, 102524, 709108, 5199577, 40199275, 326243789, 2769188430, 24508288464, 225570446906, 2154131007384, 21301873753284, 217748265668317, 2297212160044441] "" "Class ", 1886, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2280, 12746, 76099, 481808, 3217680, 22570540, 165715106, 1269835103, 10130560871, 83965576137, 721677680291, 6421572697480, 59067748329562, 560899813505760] "" "Class ", 1887, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1888, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1889, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1890, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1891, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1892, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1893, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2521, 14882, 94494, 639492, 4581090, 34554225, 273273585, 2258133761, 19439486920, 173904914869, 1613185846430, 15487230008014, 153619906395243, 1571999662700424] "" "Class ", 1894, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 92, 424, 2109, 11172, 62461, 366204, 2240791, 14257328, 94046433, 641568864, 4516813730, 32758556372, 244363646874, 1872258358251, 14715653098328, 118523229061377] "" "Class ", 1895, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 1896, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 1897, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 1898, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 1899, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 1900, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 1901, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 449, 2348, 13229, 79482, 505392, 3381137, 23691607, 173227005, 1317624762, 10398949264, 84963185462, 717235360913, 6244949461461, 55996759620951, 516373825831083] "" "Class ", 1902, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2086, 10964, 60752, 352518, 2131501, 13376227, 86843562, 581749729, 4011970797, 28429396058, 206654595129, 1538712661109, 11720510595130, 91224955266057] "" "Class ", 1903, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1904, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 378, 1651, 7360, 33418, 154360, 723977, 3439831, 16520052, 80052170, 390878699, 1921255180, 9498717434, 47206819760, 235704832666, 1181822784941] "" "Class ", 1905, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1906, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1907, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1908, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[3, 4, 2, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 0, 1]]} "Class ", 1909, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2362, 13446, 82176, 534929, 3686326, 26763760, 203909661, 1624870421, 13503849873, 116759204719, 1048068422545, 9748351892395, 93795611433052, 932146541226196] "" "Class ", 1910, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1964, 9857, 51302, 274877, 1508160, 8439704, 48022879, 277185149, 1619808425, 9568822985, 57069507779, 343275787099, 2080614068054, 12697650127690] "" "Class ", 1911, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1912, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1913, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1914, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1915, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1916, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1917, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2462, 14508, 92117, 624581, 4491994, 34085112, 271681609, 2266415579, 19727004115, 178679402777, 1680276144365, 16372040911216, 164992430508918, 1716999259457062] "" "Class ", 1918, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [ [2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 412, 2024, 10710, 60608, 364569, 2319256, 15539334, 109274293, 804095951, 6175480740, 49386676050, 410429346529, 3538029971551, 31583532715703, 291529701148917] "" "Class ", 1919, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 1920, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 382, 1718, 8072, 39618, 203190, 1088928, 6094624, 35589388, 216555884, 1371132956, 9020095144, 61564683000, 435340343264, 3185071829560, 24079675373992] "" "Class ", 1921, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "Class ", 1922, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 1923, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "Class ", 1924, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 1925, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 376, 1621, 7064, 30973, 136240, 599861, 2639176, 11587597, 50726144, 221276101, 961538008, 4161767261, 17942311888, 77058032341, 329739209960] "" "Class ", 1926, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1927, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2563, 15311, 98514, 676478, 4923460, 37774180, 304181766, 2561664744, 22493047937, 205394145397, 1946114839920, 19095745090074, 193703452478262, 2028132441784965] "" "Class ", 1928, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2284, 12831, 77230, 494313, 3344647, 23810715, 177655552, 1384715418, 11244108609, 94896016810, 830688199405, 7528537279822, 70529052760823, 682000310107924] "" "Class ", 1929, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 1930, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 1931, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[4, 1, 3, 2, 5], {1, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 1, 3, 2, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 2, 3], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2274, 12758, 76803, 492551, 3346341, 23975260, 180464208, 1422515796, 11709867667, 100418501282, 895157795373, 8278759739791, 79295621685583, 785344768256694] "" "Class ", 1932, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 1989, 10181, 54632, 305476, 1772283, 10635341, 65854929, 419979204, 2754369685, 18554457539, 128254942680, 908941001028, 6599626046737, 49062424616511] "" "Class ", 1933, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 1934, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, %1], [[1, 4, 2, 3], {2, 3}, %1], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {3}, %1], [[3, 1, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, %1], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [3, 1, 5, 2, 4], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 382, 1709, 7887, 37284, 179640, 878967, 4355690, 21815505, 110257097, 561609171, 2880104005, 14858295448, 77058247029, 401522204186, 2101018221344] "" "Class ", 1935, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2550, 15186, 97361, 665716, 4821003, 36779212, 294318656, 2461751360, 21457899639, 194420482384, 1827060399768, 17773917215281, 178686803793649, 1853617238206220] "" "Class ", 1936, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 431, 2234, 12636, 77046, 501787, 3467319, 25286909, 193797613, 1555144647, 13026315082, 113593139593, 1028881634621, 9660182776166, 93850015158315, 941926575636992] "" "Class ", 1937, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 1938, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 1939, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 1940, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 398, 1879, 9402, 49570, 273946, 1579805, 9471488, 58858859, 378220388, 2508219763, 17137660226, 120468010214, 870090441282, 6449482444399, 49011506371898] "" "Class ", 1941, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [ [3, 1, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}], [[4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1959, 9886, 52174, 286443, 1629371, 9571752, 57913755, 360077085, 2296015756, 14989045391, 100032283730, 681552751167, 4735267385305, 33513876743675] "" "Class ", 1942, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 1, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 5, 4, 2], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 380, 1678, 7584, 34875, 162560, 766124, 3644066, 17469863, 84324840, 409471090, 1998933556, 9804748548, 48298256084, 238840150970, 1185256302910] "" "Class ", 1943, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2413, 13978, 87080, 578462, 4070430, 30179123, 234752856, 1909064627, 16182660307, 142625741108, 1304093280870, 12346480813481, 120825554958759, 1220372868129503] "" "Class ", 1944, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 2000, 10378, 56967, 328606, 1981326, 12432794, 80901370, 544271046, 3776130912, 26959412016, 197693451038, 1486562112777, 11446119455151, 90128897405143] "" "Class ", 1945, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 1946, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 1, 4, 2, 5], {3, 4}, %1], [[3, 1, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[4, 1, 3, 2, 5], {3, 4}, %1], [[4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 3, 2], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3}, %1], [[5, 1, 3, 2, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3}, %1]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 364, 1517, 6296, 25914, 105724, 427998, 1721958, 6896115, 27528677, 109658063, 436238587, 1734139331, 6891027151, 27379444336, 108783352357] "" "Class ", 1947, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {1, 3}, {}], [[4, 1, 3, 2, 5], {1, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 4, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 412, 2007, 10401, 56878, 326225, 1953312, 12164979, 78567634, 524925971, 3620527731, 25733129028, 188187436437, 1414096431208, 10905308135244, 86218893469989] "" "Class ", 1948, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 381, 1695, 7760, 36328, 173127, 837157, 4097290, 20258687, 101042951, 507769856, 2568489577, 13067637917, 66825307792, 343297880852, 1770865293658] "" "Class ", 1949, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 1950, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 1, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 3, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 87, 352, 1428, 5766, 23124, 92116, 364845, 1438478, 5652199, 22155165, 86698504, 338905806, 1323905984, 5169741892, 20183387612, 78791958908] "" "Class ", 1951, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 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, 6, 22, 94, 452, 2381, 13596, 83347, 543846, 3754972, 27302167, 208193070, 1659425106, 13786095849, 119083661803, 1067246827755, 9905256171182, 95045336197008, 941480472423245] "" "Class ", 1952, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 413, 2026, 10663, 59996, 359694, 2288569, 15388537, 108931232, 808942410, 6282545204, 50886132650, 428791386596, 3750936430132, 33997875733018, 318744999572945] "" "Class ", 1953, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1954, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1955, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3, 4}, %1], [[1, 5, 2, 3, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 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]}], [[4, 1, 2, 3, 5], {1, 3, 4}, %1], [[4, 1, 3, 2, 5], {1, 3, 4}, %1], [[5, 1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1962, 9972, 53471, 301415, 1781287, 11014088, 71136345, 479214842, 3362759293, 24550497579, 186258051704, 1466763283477, 11975706912453, 101262766259403] "" "Class ", 1956, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}] , [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[1, 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, 6, 22, 89, 381, 1698, 7828, 37249, 182832, 925338, 4826443, 25926279, 143330565, 814970508, 4763059796, 28596518745, 176263380441, 1114724515860, 7228755661708] "" "Class ", 1957, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1958, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1959, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]} "Class ", 1960, " is:" {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 87, 349, 1393, 5515, 21694, 85003, 332493, 1300405, 5090717, 19959877, 78408568, 308647143, 1217503244, 4812534494, 19060931058, 75638611493] "" "Class ", 1961, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 502, 2882, 18264, 126068, 938946, 7489272, 63579870, 571570134, 5417744898, 53946694184, 562498509730, 6124554247480, 69462921014004, 818850289644242, 10013272987554916] "" "Class ", 1962, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 1963, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 1964, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 1965, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2571, 15525, 101913, 720975, 5458672, 43978389, 375217521, 3376238521, 31926215463, 316286134599, 3273752642593, 35317690116979, 396258754622477, 4614872623587290] "" "Class ", 1966, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2267, 12637, 75340, 477167, 3194198, 22509149, 166435885, 1287768035, 10401714210, 87526659221, 765814955219, 6955112823304, 65461551596345, 637562773779512] "" "Class ", 1967, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 1968, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 1969, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 2, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 1, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 483, 2725, 16947, 114763, 838124, 6551172, 54473828, 479432140, 4447267865, 43322237710, 441790577574, 4703456736840, 52150675049766, 600907801790694, 7181604801221235] "" "Class ", 1970, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 5, 1], {2, 4}, {}], [[2, 5, 3, 4, 1], {2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2442, 14297, 90159, 606464, 4318034, 32343058, 253579052, 2072460097, 17595143297, 154723001729, 1405642415328, 13164407744126, 126853408298119, 1255578240181177] "" "Class ", 1971, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 1972, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 1973, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 1, 5, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 1, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 443, 2335, 13420, 83200, 552002, 3894749, 29073135, 228606357, 1886530192, 16286911570, 146694224122, 1375090815555, 13386229567529, 135069785886195, 1410198796003584] "" "Class ", 1974, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2126, 11361, 64228, 381357, 2364848, 15247758, 101852168, 702743736, 4995669976, 36511487957, 273842952034, 2104314111076, 16544054931460, 132908072352522] "" "Class ", 1975, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2181, 12030, 71182, 448741, 2997674, 21124712, 156447457, 1213673841, 9834669852, 83034709705, 728856722470, 6638196514486, 62619948576947, 610847538821697] "" "Class ", 1976, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 1977, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 493, 2809, 17657, 120900, 893061, 7063421, 59452411, 529833085, 4978111298, 49130873120, 507726612474, 5478786535431, 61581842835417, 719427899313733, 8718454867896295] "" "Class ", 1978, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 1979, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 1980, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 1981, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2460, 14534, 92978, 638456, 4673278, 36256803, 296746941, 2552006036, 22982369842, 216094148575, 2115945167378, 21527278057904, 227099925746915, 2479705588515699] "" "Class ", 1982, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2145, 11600, 66785, 406702, 2606803, 17518561, 123056064, 901196354, 6866301833, 54327694998, 445679423760, 3785396093634, 33245385391133, 301559729062740] "" "Class ", 1983, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 1984, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 1985, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 3, 1, 2], {1}, {}], [[4, 3, 2, 1], {1}, {}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2763, 17430, 120152, 895764, 7163632, 61050741, 551462695, 5255823074, 52649187209, 552494896438, 6056143852101, 69166027554599, 821185050893152, 10115059408156060] "" "Class ", 1986, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 1987, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 1988, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 1989, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2623, 16144, 108483, 788301, 6146820, 51107321, 450702794, 4196855187, 41106832535, 422097464610, 4530580118793, 50701432914235, 590227574878284, 7132863431694203] "" "Class ", 1990, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2184, 12096, 72104, 459440, 3111616, 22292592, 168263312, 1333377904, 11059335280, 95753379216, 863373139824, 8089902823120, 78625465178608, 791248858589264] "" "Class ", 1991, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 444, 2354, 13664, 85892, 579812, 4175201, 31896062, 257315604, 2183550427, 19425093233, 180630110494, 1751149914842, 17659134995796, 184859622708687, 2005141925119364] "" "Class ", 1992, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 1993, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 2]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 2]}], [[3, 1, 2], {1}, {[0, 0, 0, 2]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 382, 1705, 7823, 36636, 174294, 839616, 4085873, 20051163, 99099049, 492749932, 2462947752, 12367115012, 62349252238, 315463387335, 1601246530854] "" "Class ", 1994, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "Class ", 1995, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} "Class ", 1996, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 3}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2705, 16799, 113809, 833110, 6539444, 54698372, 484995516, 4538513884, 44653841990, 460414303856, 4960633167622, 55708793664726, 650625055350856, 7886476216592946] "" "Class ", 1997, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 1998, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "Class ", 1999, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 2000, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {2, 3}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 2001, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 2002, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 479, 2666, 16314, 108437, 775839, 5933426, 48224483, 414540437, 3753552462, 35676464796, 354870626265, 3684292114196, 39830266723855, 447442338946302, 5213244732907741] "" "Class ", 2003, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2004, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2005, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2006, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 445, 2360, 13689, 86037, 581382, 4197495, 32212882, 261612430, 2239868392, 20150261786, 189916072234, 1870409101757, 19204185573706, 205130923037660, 2275204674340405] "" "Class ", 2007, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 0, 1], [0, 0, 1, 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, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 398, 1876, 9334, 48663, 264446, 1492304, 8721011, 52669070, 328180703, 2107049981, 13924649075, 94637073534, 660966435100, 4740762442002, 34898028449216] "" "Class ", 2008, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2009, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 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, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1}, {}], [[3, 4, 1, 2, 5], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 1, 2, 4], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 380, 1678, 7584, 34875, 162560, 766124, 3644066, 17469863, 84324840, 409471090, 1998933556, 9804748548, 48298256084, 238840150970, 1185256302910] "" "Class ", 2010, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2011, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2012, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2013, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2014, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [ [2, 4, 1, 5, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}] , [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2085, 10962, 60816, 353754, 2146622, 13533714, 88355598, 595650296, 4136720314, 29535215672, 216406850448, 1624691962994, 12480751119347, 97981917700604] "" "Class ", 2015, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [ [2, 4, 1, 5, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}] , [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1960, 9906, 52424, 289017, 1653393, 9784274, 59738800, 375497214, 2425249452, 16068867963, 109057635103, 757182062281, 5371646508024, 38897010599588] "" "Class ", 2016, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[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, 6, 22, 90, 393, 1791, 8415, 40470, 198292, 986634, 4973257, 25348589, 130452875, 677046899, 3540113116, 18633157627, 98655097725, 525114137681, 2808424787327] "" "Class ", 2017, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {2, 4}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {4}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [2, 4, 5, 1, 3], {2, 4, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 378, 1646, 7267, 32358, 144950, 652430, 2948916, 13380177, 60932337, 278458616, 1276879198, 5874442946, 27112002766, 125511301142, 582742581157] "" "Class ", 2018, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2585, 15632, 102477, 722117, 5431637, 43360194, 365625034, 3243752468, 30175525317, 293479567079, 2976436746897, 31406713268301, 344092088302464, 3907175053389387] "" "Class ", 2019, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 2020, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 2021, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 2022, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 429, 2198, 12220, 72972, 464332, 3128816, 22213487, 165465955, 1288548935, 10458225403, 88231264579, 771938144924, 6989490791302, 65375995916017, 630653588455924] "" "Class ", 2023, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 2024, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 2025, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 2026, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2836, 17998, 124606, 931820, 7468606, 63755512, 576618866, 5500881236, 55145210544, 579025771201, 6349869252427, 72546756589732, 861567610731846, 10614837157637645] "" "Class ", 2027, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {2, 3}, {}], [[1, 2, 5, 3, 4], {2, 3}, {}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 5, 4, 2], {1, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2450, 14486, 93121, 645690, 4797891, 37997093, 319221760, 2833452001, 26477507930, 259663546406, 2665020839641, 28553177141205, 318631067786769, 3695812175931361] "" "Class ", 2028, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2029, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2030, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [ [2, 4, 1, 3, 5], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2476, 14861, 97508, 692820, 5289169, 43104996, 372982671, 3410973289, 32838903237, 331695573464, 3504587810817, 38631255990754, 443231969383164, 5282100957651731] "" "Class ", 2031, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[1, 0, 0, 0, 0, 0]}], [ [2, 4, 1, 3, 5], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2133, 11512, 66332, 405762, 2623064, 17851077, 127468493, 952299010, 7424602910, 60272849038, 508440074044, 4448714757285, 40307608557993, 377608585783432] "" "Class ", 2032, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2033, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2034, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {2}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 2, 5, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 5, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 489, 2761, 17143, 115763, 842123, 6551630, 54183184, 473993439, 4367615437, 42239526713, 427407363409, 4512634330754, 49595163443700, 566162906506042, 6700475418755551] "" "Class ", 2035, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2425, 14103, 88308, 590440, 4188251, 31354388, 246651048, 2031350756, 17459243177, 156171612867, 1450291836171, 13952236835727, 138779504561129, 1424763283768166] "" "Class ", 2036, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2037, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2038, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622] "" "Class ", 2039, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 2040, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2041, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 2, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 1]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 1]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 1, 1]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 4, 1, 3, 5], {1, 3, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1, 1]}], [[3, 4, 1, 2, 5], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1, 1]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1, 1]}], [[4, 5, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1, 1]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 392, 1775, 8251, 39094, 187981, 914690, 4494902, 22274721, 111188076, 558557403, 2821781898, 14327202897, 73073406990, 374220388308, 1923543399775] "" "Class ", 2042, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {2}, %1], [[3, 1, 5, 4, 2], {3, 4}, %1], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {4}, %1], [[3, 2, 5, 4, 1], {3}, %1], [[4, 1, 2, 5, 3], {2, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 3, 5, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 5, 1], {2}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 1, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 483, 2735, 17114, 116806, 861060, 6803121, 57249826, 510480023, 4801981222, 47475729145, 491725522537, 5320358309716, 59984397750711, 703150100266503, 8552728644296828] "" "Class ", 2043, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 2044, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 2045, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 2046, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 2047, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 2048, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 2049, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 2050, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 1, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 1, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2613, 16042, 107528, 779569, 6066103, 50344144, 443284635, 4122538158, 40338680351, 413906081272, 4440514440382, 49681309698177, 578338635547947, 6990476447458713] "" "Class ", 2051, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2052, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2053, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2054, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [ [2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 429, 2202, 12306, 74358, 482620, 3346824, 24681638, 192766645, 1588635982, 13770289512, 125178532908, 1190300010707, 11811518845867, 122055467442506, 1310914556598526] "" "Class ", 2055, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [ [2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 401, 1913, 9671, 51467, 287030, 1672116, 10151095, 64102795, 420461213, 2861041189, 20173973726, 147256928534, 1111564837559, 8668154634356, 69759860995017] "" "Class ", 2056, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "Class ", 2057, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[3, 4, 2, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 0, 1], [0, 0, 2, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 2, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1}, {}], [[2, 4, 1, 3, 5], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0]}], [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 2, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 2, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 366, 1548, 6592, 28142, 120234, 513754, 2195100, 9378034, 40062340, 171135208, 731021190, 3122582506, 13338119262, 56973614692, 243361758882] "" "Class ", 2058, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2059, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2060, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2061, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2062, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {2, 3}, {[0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [3, 4, 1, 5, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 421, 2069, 10815, 59699, 345978, 2095746, 13223835, 86674195, 588702512, 4135039588, 29982305023, 224063479000, 1723428241159, 13626662002729, 110629386865687] "" "Class ", 2063, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [ [3, 4, 1, 5, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 378, 1644, 7217, 31701, 138628, 601884, 2591277, 11058206, 46780868, 196255104, 816871562, 3375192811, 13851250308, 56487188424, 229030237147] "" "Class ", 2064, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 2, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[3, 4, 1, 2], {3}, {[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, 6, 22, 89, 375, 1605, 6907, 29767, 128289, 552687, 2380103, 10246549, 44102931, 189801119, 816760289, 3514549639, 15122823679, 65071296869, 279989913851] "" "Class ", 2065, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 2, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {[0, 0, 2, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {1, 2, 3}, {[0, 0, 2, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 3, 5, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 2, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {4}, {[0, 0, 0, 2, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 361, 1480, 6006, 24058, 95119, 371582, 1436190, 5499678, 20892147, 78820344, 295615604, 1103099988, 4098388395, 15170119516, 55972005848] "" "Class ", 2066, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2587, 15675, 103005, 727156, 5474092, 43685791, 367777445, 3252761198, 30116596693, 291016400291, 2927024261918, 30571040574669, 330873468187169, 3703999221946968] "" "Class ", 2067, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 2068, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 2069, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {3, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 3, 4, 5], {3}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 4, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 1, 4, 5], {3}, {[0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 4, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 1, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {2, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1807, 8583, 41945, 210051, 1074997, 5611724, 29837438, 161399216, 887364470, 4954638790, 28075438045, 161352922121, 939988568493, 5548129984175] "" "Class ", 2070, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2168, 11915, 70271, 441498, 2936812, 20576884, 151205623, 1161093884, 9288368333, 77202552722, 665180839594, 5928976541248, 54571673176866, 517846924104182] "" "Class ", 2071, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 2072, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 5, 2, 1, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1808, 8596, 42034, 210330, 1072912, 5563279, 29255407, 155735793, 837959495, 4551649325, 24932955861, 137612150695, 764704340585, 4275687579461] "" "Class ", 2073, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 2074, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {[0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 360, 1464, 5854, 22940, 88088, 331852, 1228566, 4477512, 16090936, 57107120, 200424158, 696429604, 2398412904, 8193798468, 27791128630] "" "Class ", 2075, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 5, 4], {2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {2}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 2, 5, 3], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 3, 5, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 479, 2673, 16393, 109084, 780060, 5949034, 48092938, 410067387, 3672372269, 34419539246, 336584340196, 3424916216578, 36178526689769, 395905273048072, 4479850792589316] "" "Class ", 2076, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 451, 2384, 13678, 84279, 552975, 3837596, 28015274, 214166654, 1708037679, 14166331902, 121860231861, 1084688159458, 9970383279292, 94474909388002, 921385826200953] "" "Class ", 2077, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 2078, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 2079, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3, 4}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {[1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622] "" "Class ", 2080, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 1, 5], {2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3}, {}], [ [3, 4, 5, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 2081, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 2082, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 2083, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 2084, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2322, 13307, 82307, 544659, 3828490, 28418062, 221677235, 1809878427, 15413156460, 136513023127, 1254283862780, 11928787808142, 117200797133509, 1187543541200935] "" "Class ", 2085, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 2086, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 2087, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 2088, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {1, 2}, %1], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 3, 1, 5], {2}, {}], [[2, 4, 5, 1, 3], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 3}, %1], [[2, 5, 4, 1, 3], {1, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {4}, {}], [[3, 5, 4, 1, 2], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 2, 3, 1, 5], {1}, {[0, 0, 1, 0, 0, 0]}], [[5, 2, 3, 1, 4], {2, 3}, %1], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1970, 9947, 52224, 282923, 1572641, 8931095, 51650058, 303396594, 1806470594, 10884420117, 66272829085, 407307440990, 2524322685567, 15763214253065] "" "Class ", 2089, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 2090, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 2091, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2092, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2194, 12301, 74949, 493209, 3485866, 26328838, 211567100, 1801411999, 16193840706, 153190522005, 1520425527643, 15789717571886, 171155489251102, 1932153674637367] "" "Class ", 2093, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2094, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 2095, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[1, 0, 0, 0]}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}] , [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 429, 2196, 12217, 73341, 472288, 3246267, 23713813, 183394955, 1496400945, 12842205745, 115597595304, 1088620675057, 10701015988483, 109568364350339, 1166344682981878] "" "Class ", 2096, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 2097, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 2098, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 2099, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2100, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {}, {}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 1, 5], {3}, {}], [[2, 3, 5, 1, 4], {3}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2}, {}], [[2, 4, 5, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2}, {}], [[3, 4, 2, 1, 5], {3}, {}], [[3, 4, 2, 5, 1], {3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 4, 5, 2, 1], {3}, {}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2150, 11709, 68313, 424501, 2795680, 19426176, 141843179, 1084305866, 8649558110, 71793020920, 618471345643, 5517511515455, 50874902963167, 484000120640764] "" "Class ", 2101, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2102, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2103, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [3, 4, 1, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2095, 11049, 61559, 360094, 2201204, 14010819, 92592183, 633796890, 4484387627, 32739097235, 246246489748, 1905547517996, 15152548106152, 123677249720543] "" "Class ", 2104, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {4}, {[0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {[1, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [ [3, 4, 1, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 393, 1789, 8374, 39957, 193226, 943207, 4634435, 22875823, 113277124, 562168943, 2794149577, 13902024795, 69215279442, 344758950712, 1717688255084] "" "Class ", 2105, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2106, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]} "Class ", 2107, " is:" {{[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2108, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 469, 2482, 13960, 82349, 504828, 3194759, 20765507, 138085776, 936489543, 6461176120, 45256388216, 321266564830, 2308053336011, 16760746522369, 122901529451504] "" "Class ", 2109, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 434, 2179, 11567, 64155, 368657, 2181282, 13227315, 81909378, 516484595, 3308599462, 21492017358, 141344563801, 939900672286, 6312543933036, 42779420926636] "" "Class ", 2110, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2111, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 1]}], [[3, 4, 2, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1955, 9799, 50987, 273360, 1501581, 8414253, 47937766, 276948216, 1619132064, 9563466350, 56993108920, 342320988368, 2070430224309, 12600242220981] "" "Class ", 2112, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2208, 11873, 66983, 393015, 2382517, 14847230, 94734830, 616947123, 4090155495, 27546344594, 188128155225, 1300962161734, 9098073448955, 64274657296640] "" "Class ", 2113, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 408, 1938, 9615, 49354, 260359, 1404687, 7722264, 43135238, 244268319, 1399801325, 8105718991, 47371292042, 279123783658, 1656778588642, 9899228458769] "" "Class ", 2114, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2115, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 1]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 2116, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 3, 4, 5], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 458, 2389, 13239, 76934, 464575, 2895927, 18540657, 121441870, 811275324, 5513588877, 38042852087, 266037193476, 1882865988816, 13470269415473, 97310913252151] "" "Class ", 2117, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 435, 2194, 11720, 65488, 379397, 2264225, 13852732, 86561195, 550819813, 3561005572, 23344214597, 154931687131, 1039629941168, 7045421385497, 48173519366929] "" "Class ", 2118, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 1, 5, 2], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2100, 10979, 59851, 337329, 1953753, 11576418, 69935266, 429632218, 2678398391, 16916269606, 108090755845, 697958293843, 4549948502450, 29919832321709] "" "Class ", 2119, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1953, 9760, 50513, 268713, 1461198, 8088655, 45439524, 258425487, 1485121443, 8611189550, 50317070033, 296000187371, 1751626714150, 10420087621893] "" "Class ", 2120, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2087, 10875, 59205, 334130, 1943360, 11596003, 70734861, 439831882, 2781344892, 17852555289, 116124197993, 764415900386, 5086466983372, 34178096527032] "" "Class ", 2121, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 408, 1938, 9615, 49354, 260359, 1404687, 7722264, 43135238, 244268319, 1399801325, 8105718991, 47371292042, 279123783658, 1656778588642, 9899228458769] "" "Class ", 2122, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 2, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1970, 9951, 52316, 284205, 1586791, 9067870, 52866529, 313631748, 1889326723, 11536833164, 71306320139, 445552660747, 2811551637748, 17901077927356] "" "Class ", 2123, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 460, 2419, 13544, 79637, 487025, 3076230, 19963604, 132573461, 898025814, 6189063512, 43307035076, 307142045510, 2204648342116, 15996582725282, 117205827359726] "" "Class ", 2124, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2210, 11903, 67287, 395654, 2403744, 15011028, 95969158, 626121474, 4157810085, 28043123779, 191768623633, 1327624762094, 9293414293443, 65707083544575] "" "Class ", 2125, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 2126, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 2, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 2127, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2223, 12022, 68248, 403007, 2458663, 15417135, 98963778, 648225570, 4321457223, 29259595129, 200852448878, 1395778280611, 9807174954950, 69597909367356] "" "Class ", 2128, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1971, 9970, 52542, 286392, 1605728, 9221360, 54059745, 322656058, 1956316523, 12027744424, 74871508789, 471281314080, 2996409355323, 19225253511378] "" "Class ", 2129, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 2130, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2314, 12718, 73416, 440958, 2736636, 17456381, 113979597, 759323649, 5147789731, 35439230312, 247316482904, 1746979810552, 12475230234634, 89965177016720] "" "Class ", 2131, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1974, 10031, 53315, 294323, 1678166, 9837814, 59072344, 362194616, 2261774588, 14353820310, 92407493855, 602560354287, 3974467909584, 26488374629107] "" "Class ", 2132, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 2133, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 382, 1711, 7922, 37663, 182936, 904302, 4535994, 23034564, 118209806, 612165222, 3195359360, 16795435994, 88825567814, 472356139660, 2524292893556] "" "Class ", 2134, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 435, 2194, 11730, 65690, 382036, 2292590, 14126431, 89033532, 572215728, 3740881702, 24826290599, 166969988466, 1136413309601, 7817751578247, 54303412996184] "" "Class ", 2135, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1838, 8889, 44418, 227948, 1195995, 6393614, 34731157, 191300940, 1066561180, 6010428305, 34194819122, 196207962099, 1134503734366, 6605604909451] "" "Class ", 2136, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 2137, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 382, 1711, 7922, 37663, 182936, 904302, 4535994, 23034564, 118209806, 612165222, 3195359360, 16795435994, 88825567814, 472356139660, 2524292893556] "" "Class ", 2138, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 457, 2375, 13099, 75724, 454827, 2820139, 17962193, 117066213, 778295498, 5265122649, 36168205671, 251856739323, 1775253964179, 12650702483745, 91045742453820] "" "Class ", 2139, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 2140, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 2, 4, 1, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 2, 5, 1, 3], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {1, 2, 3}, {}], [[4, 3, 5, 2, 1], {1}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 445, 2269, 12237, 68954, 402480, 2418188, 14884370, 93512004, 597914388, 3881786953, 25539882495, 170027011733, 1143822235785, 7767113250052, 53187762538274] "" "Class ", 2141, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2074, 10754, 58202, 326240, 1882960, 11140560, 67329992, 414499438, 2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316] "" "Class ", 2142, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {2}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 433, 2164, 11414, 62828, 358065, 2100588, 12629101, 77545756, 484953752, 3081948096, 19866848214, 129699785370, 856423347008, 5713374699257, 38471209755921] "" "Class ", 2143, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 2144, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {2}, {}], [[3, 1, 4, 2], {1, 3}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 420, 2040, 10374, 54650, 296058, 1640648, 9264124, 53142918, 308976682, 1817356208, 10797863286, 64727054678, 391058589620, 2379221431408, 14566354602622] "" "Class ", 2145, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 2146, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {2}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 445, 2267, 12227, 69004, 404056, 2439561, 15114973, 95741795, 618154357, 4058283448, 27037988573, 182505050420, 1246351033831, 8601194257599, 59922755611039] "" "Class ", 2147, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 407, 1924, 9480, 48198, 251046, 1332971, 7189150, 39278559, 216948153, 1209418859, 6796103357, 38455196532, 218923813350, 1253049757584, 7206512598533] "" "Class ", 2148, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2149, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1809, 8611, 42156, 210979, 1074535, 5550534, 29006221, 153063247, 814417461, 4364437270, 23535357165, 127615441575, 695358749202, 3805518972023] "" "Class ", 2150, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2151, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2152, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2153, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 3, 4, 5], {2}, %1], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2}, %1], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2}, %1], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 2, 3, 4], {2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2}, {[0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 443, 2242, 11970, 66660, 384083, 2276129, 13811242, 85511762, 538746702, 3446266361, 22342553617, 146583474014, 971983687390, 6507162489000, 43942736857883] "" "Class ", 2154, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [1, 5, 2, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 431, 2137, 11145, 60468, 338604, 1945748, 11424551, 68316205, 414980911, 2555459994, 15926955758, 100330549469, 638090828334, 4093261886285, 26463294129035] "" "Class ", 2155, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2156, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2157, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2158, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2159, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2160, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {2}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 459, 2396, 13274, 77108, 465469, 2900826, 18570443, 121644842, 812798492, 5525798744, 38144482460, 266898658819, 1890219049095, 13533101993931, 97846965935590] "" "Class ", 2161, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2119, 11207, 62111, 357598, 2124986, 12968452, 80965148, 515512584, 3339048144, 21956094323, 146317006591, 986777831582, 6726689028648, 46300942813751] "" "Class ", 2162, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 2163, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 380, 1678, 7583, 34854, 162297, 763559, 3622519, 17305881, 83160804, 401621439, 1948029017, 9484571489, 46332953040, 227013403727, 1115237865753] "" "Class ", 2164, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 2165, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 2166, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 2167, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 457, 2382, 13179, 76447, 460769, 2867106, 18326216, 119860862, 799658332, 5428247708, 37414901824, 261404552855, 1848581110178, 13215669372288, 95413624085343] "" "Class ", 2168, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 421, 2059, 10604, 56940, 316561, 1812730, 10648850, 63969972, 391935635, 2443804633, 15478298829, 99423986912, 646799485552, 4256331105633, 28302856289534] "" "Class ", 2169, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2170, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2171, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2172, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2173, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2174, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 458, 2393, 13287, 77410, 468932, 2933917, 18861924, 124105143, 833069319, 5690459347, 39470895256, 277532780913, 1975265464203, 14212608691671, 103276310421507] "" "Class ", 2175, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [ [4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2085, 10833, 58658, 328388, 1889832, 11131469, 66883286, 408849005, 2537200093, 15956092362, 101540929691, 653074244336, 4240680921241, 27776032125086] "" "Class ", 2176, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2177, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2178, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2179, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {3}, {[0, 0, 0, 1]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {2, 4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 2180, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2181, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 3}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2320, 12794, 74124, 446809, 2782443, 17806002, 116619012, 779183025, 5297327274, 36568535542, 255879706610, 1812211046640, 12974511629496, 93804913979127] "" "Class ", 2182, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1956, 9820, 51266, 276384, 1530708, 8673844, 50128277, 294706327, 1758814339, 10637024993, 65096690936, 402626910706, 2514183497832, 15836179615029] "" "Class ", 2183, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 2184, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 2185, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 2186, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 2187, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 2188, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2189, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 406, 1915, 9411, 47771, 248832, 1323999, 7170943, 39428831, 219622478, 1237170858, 7038351726, 40392934713, 233624670613, 1360697417545, 7975103180141] "" "Class ", 2190, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2191, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 366, 1555, 6718, 29497, 131493, 593880, 2711062, 12484428, 57911104, 270316632, 1268717574, 5983656823, 28343205411, 134777104601, 643132762633] "" "Class ", 2192, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2193, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2194, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "Class ", 2195, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {2}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 0, 1]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 4, 3], {2}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 5, 4, 2], {3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 5, 1, 4, 2], {2, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 5, 2, 4, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 338, 1318, 5110, 19770, 76466, 295810, 1144530, 4428622, 17136186, 66306722, 256565926, 992749334, 3841316550, 14863484902, 57512368162] "" "Class ", 2196, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {}], [[4, 5, 2, 1, 3], {1, 2}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 433, 2162, 11429, 63246, 363292, 2152372, 13089852, 81410463, 516230723, 3329360100, 21794953778, 144577885686, 970480696133, 6584031675894, 45099586564749] "" "Class ", 2197, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1799, 8455, 40587, 198088, 980187, 4908389, 24842258, 126955428, 654624306, 3403614912, 17834390471, 94130866561, 500225608845, 2675334110619] "" "Class ", 2198, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2199, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2200, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2201, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2202, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2203, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {2}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2230, 12111, 69062, 409610, 2509626, 15801840, 101840119, 669664083, 4481307957, 30454254449, 209811080130, 1463222214502, 10317036147048, 73468659210199] "" "Class ", 2204, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 3, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 395, 1834, 8918, 45035, 234607, 1254210, 6853090, 38152638, 215873668, 1238891591, 7199517615, 42306666414, 251098194829, 1503757598663, 9079105435207] "" "Class ", 2205, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 2206, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 365, 1537, 6513, 27666, 117602, 499841, 2123385, 9014173, 38237478, 162072153, 686413070, 2904888698, 12284358742, 51912067904, 219225637504] "" "Class ", 2207, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "Class ", 2208, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 2209, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 366, 1554, 6687, 29065, 127363, 561931, 2493746, 11122340, 49822012, 224017900, 1010591421, 4572225893, 20739273976, 94286581644, 429528054476] "" "Class ", 2210, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 2211, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 330, 1206, 4174, 13726, 43134, 130302, 380414, 1078270, 2978814, 8046590, 21311486, 55468030, 142147582, 359268350, 896794622] "" "Class ", 2212, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 449, 2333, 12920, 75200, 455503, 2850878, 18338267, 120738385, 811027131, 5543724256, 38479138903, 270736602468, 1928106193769, 13881611641532, 100928824363328] "" "Class ", 2213, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2095, 11011, 60735, 348578, 2067918, 12615096, 78812596, 502606407, 3263152615, 21521909640, 143938351824, 974696918304, 6674304092526, 46165014861264] "" "Class ", 2214, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 2215, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 2216, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {3, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 4, 1], {1}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 3}, {}], [[3, 5, 4, 1, 2], {1, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}], [ [4, 1, 3, 2, 5], {1, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[5, 1, 3, 2, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 2, 3], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 2, 4, 3, 1], {3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 420, 2046, 10474, 55778, 306740, 1732546, 10009408, 58957342, 353146146, 2146602566, 13218561498, 82343975082, 518289616468, 3292779235132, 21097056912476] "" "Class ", 2217, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 2218, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 2219, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2317, 12757, 73783, 444017, 2760736, 17641211, 115380041, 769889617, 5227509569, 36042145337, 251892863737, 1781864542583, 12742351287291, 92019933758264] "" "Class ", 2220, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 412, 2007, 10379, 56354, 318449, 1860101, 11171720, 68706538, 431270428, 2755690461, 17885653797, 117705855359, 784261938672, 5283781342387, 35956738145932] "" "Class ", 2221, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 2222, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 2223, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 2224, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 4, 1, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 5, 3, 1, 4], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 2, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 381, 1694, 7744, 36168, 171831, 827814, 4034589, 19857262, 98555324, 492710856, 2478897620, 12541604830, 63768192378, 325674039636, 1669922290311] "" "Class ", 2225, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[2, 4, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 1, 3], {1, 3}, {}], [[3, 1, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1}, {}], [[3, 5, 4, 1, 2], {1, 3}, {}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 2, 5, 3, 1], {1}, {}], [[5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 1, 3], {2, 3}, {}], [[5, 3, 4, 1, 2], {2, 3}, {}], [[5, 3, 4, 2, 1], {4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 392, 1778, 8309, 39789, 194632, 970500, 4924957, 25399389, 132951967, 705484392, 3790558041, 20600480956, 113130880615, 627224095559, 3507899170162] "" "Class ", 2226, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2227, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1820, 8787, 44021, 227495, 1207059, 6550722, 36251940, 204069515, 1166121211, 6752907781, 39573106391, 234393981599, 1401782534495, 8456988152630] "" "Class ", 2228, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2229, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, %2], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, %2], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, %2], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {1}, %2], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 1, 4, 2, 5], {3, 4}, %1], [[3, 1, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {1, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[4, 1, 3, 2, 5], {3, 4}, %1], [[4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 3, 2], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 2, 5, 3, 1], {1, 3}, %1], [[5, 1, 3, 2, 4], {3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 3, 1], {1, 3}, %1] } %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %2 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 87, 349, 1388, 5436, 20950, 79559, 298285, 1106260, 4065745, 14830503, 53762750, 193911337, 696509890, 2493393924, 8901688358, 31710310192] "" "Class ", 2230, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 2231, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 366, 1556, 6719, 29379, 129824, 578916, 2601965, 11775705, 53618864, 245468748, 1129201321, 5217099433, 24198359988, 112637623880, 525998175542] "" "Class ", 2232, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 2233, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {}, {}], [[4, 1, 2, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 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]}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2}, {}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2203, 11812, 66440, 388518, 2346344, 14560672, 92481297, 599287901, 3951997242, 26465901618, 179675768664, 1234782393161, 8579293461847, 60202274389224] "" "Class ", 2234, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {}], [[4, 5, 2, 1, 3], {1, 2, 3}, {}], [[4, 5, 3, 1, 2], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 397, 1858, 9135, 46855, 249316, 1369433, 7730855, 44687870, 263683556, 1584172821, 9670182417, 59870924280, 375406115666, 2380896214893, 15256681662694] "" "Class ", 2235, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2236, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2237, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2238, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {[1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}] , [[3, 4, 1, 2], {1}, {[1, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[4, 1, 3, 2], {3}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 3, 1, 4], {1, 3}, {[0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 3}, {[1, 0, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 365, 1536, 6491, 27402, 115257, 482473, 2009420, 8327801, 34357400, 141172145, 578005699, 2359255940, 9604281211, 39009211924, 158134284975] "" "Class ", 2239, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2240, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]} "Class ", 2241, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 544, 3438, 24814, 201484, 1817650, 18037146, 195262904, 2289997846, 28922461740, 391380236822, 5649256566542, 86638840566488, 1406881582487954, 24114793718964602, 435096862468815162] "" "Class ", 2242, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2926, 19299, 141481, 1141753, 10062161, 96174744, 991082453, 10954686341, 129291332396, 1622884883687, 21588286519473, 303380945221003, 4491232267525536, 69861384695812811] "" "Class ", 2243, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2244, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 2245, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 5, 3, 2, 4], {2, 3}, {}], [[1, 5, 4, 2, 3], {2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3069, 20680, 154959, 1277416, 11488202, 111923618, 1174154839, 13195438323, 158152257087, 2013609670343, 27140378956295, 386060139112186, 5779484479601436, 90830820014793037] "" "Class ", 2246, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2675, 16374, 108768, 776766, 5921515, 47907448, 409362365, 3679550118, 34671013625, 341451256415, 3505500781007, 37431095905787, 414847258267503, 4763449082314406] "" "Class ", 2247, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 2248, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 2249, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 548, 3482, 25256, 206298, 1871704, 18676354, 203323724, 2397969518, 30455963576, 414446765490, 6015821216380, 92778775395190, 1515047281161392, 26114701159308242, 473827422862284740] "" "Class ", 2250, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 516, 3123, 21378, 163305, 1376605, 12691840, 127031772, 1371615647, 15890685727, 196613557049, 2587433027080, 36086361542882, 531670868848664, 8251298985467428, 134542595259910342] "" "Class ", 2251, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 2252, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 2253, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2}, {}], [[1, 5, 3, 2, 4], {2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 505, 3010, 20178, 150489, 1235551, 11067759, 107418864, 1122905300, 12577051944, 150256496484, 1907225676290, 25631387902143, 363575422929769, 5428277102767295, 85091463992085270] "" "Class ", 2254, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2512, 14745, 92979, 624486, 4438483, 33211493, 260539575, 2135470154, 18234231970, 161799764796, 1488781371340, 14178428501258, 139522649648443, 1416555138610389] "" "Class ", 2255, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 2256, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 2257, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 545, 3452, 24978, 203366, 1839704, 18306801, 198733504, 2337183561, 29600503238, 401669136255, 5813885869358, 89411516391424, 1455941727289832, 25025088399821756, 452776255394225448] "" "Class ", 2258, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3082, 20934, 158625, 1326605, 12137621, 120591516, 1292874164, 14876652363, 182863938899, 2391351000878, 33149608807709, 485551031901264, 7493091047314108, 121514965052634258] "" "Class ", 2259, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 2260, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 2261, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 516, 3112, 21190, 160791, 1344677, 12288143, 121816436, 1301954419, 14923189175, 182603364616, 2375690624769, 32746202628507, 476702710474818, 7308339848281907, 117696866033189173] "" "Class ", 2262, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2690, 16547, 110593, 795499, 6114014, 49911887, 430660981, 3911383086, 37261056649, 371179490943, 3856185453325, 41682543369624, 467803185092603, 5440890524670929] "" "Class ", 2263, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 2264, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 2265, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 522, 3157, 21567, 164173, 1378216, 12649560, 126010787, 1354035456, 15610959733, 192219066191, 2517493559159, 34945189765358, 512467892042162, 7917053632081997, 128516406776444283] "" "Class ", 2266, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2793, 17497, 119402, 879172, 6933401, 58203607, 517459610, 4851348773, 47786802869, 492978029080, 5311395214840, 59618387942831, 695648249427616, 8421388315254367] "" "Class ", 2267, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 544, 3451, 25020, 204042, 1849050, 18432294, 200446632, 2361461373, 29960374914, 407265032079, 5905214379184, 90975220961316, 1484000876515254, 25552081781989222, 463121365160181224] "" "Class ", 2268, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3080, 20872, 157498, 1309235, 11885061, 116964544, 1240224587, 14094448322, 170888228889, 2201689601201, 30036386945649, 432538447416846, 6556437450377006, 104346884820280358] "" "Class ", 2269, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 2270, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 2271, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3034, 20300, 150992, 1235583, 11032006, 106726668, 1112078635, 12416623585, 147888059985, 1871613148055, 25080714039626, 354778040274057, 5282723181932093, 82594845362563212] "" "Class ", 2272, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 3}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2675, 16374, 108768, 776766, 5921515, 47907448, 409362365, 3679550118, 34671013625, 341451256415, 3505500781007, 37431095905787, 414847258267503, 4763449082314406] "" "Class ", 2273, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 2274, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 2275, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 507, 3044, 20569, 154687, 1281507, 11587165, 113518052, 1197819969, 13541793969, 163280196552, 2091430807047, 28358815980930, 405801013623631, 6110928195658772, 96600716111946208] "" "Class ", 2276, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 2277, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 546, 3479, 25346, 207656, 1890354, 18930115, 206799612, 2447429742, 31192732896, 425951432704, 6204342000886, 96019673361656, 1573433270675524, 27215574620147633, 495522165989249162] "" "Class ", 2278, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[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, 6, 22, 98, 515, 3115, 21336, 163151, 1377231, 12718803, 127532769, 1379664509, 16015564366, 198557118529, 2618298410378, 36590691705345, 540185527557525, 8400147619693481, 137239349552528787] "" "Class ", 2279, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 2280, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 2281, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2973, 19888, 148253, 1218514, 10951286, 106833309, 1124350486, 12698400932, 153192731767, 1966127875673, 26749163726954, 384543112649468, 5824671282969951, 92718567140252932] "" "Class ", 2282, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2690, 16547, 110593, 795499, 6114014, 49911887, 430660981, 3911383086, 37261056649, 371179490943, 3856185453325, 41682543369624, 467803185092603, 5440890524670929] "" "Class ", 2283, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 2284, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 2285, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3176, 21813, 167078, 1411821, 13044806, 130816035, 1414908720, 16417587588, 203415433469, 2680312725884, 37424416961452, 551958523113108, 8574306257487939, 139931538553435655] "" "Class ", 2286, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 2287, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 567, 3679, 27254, 227172, 2104369, 21441445, 238320423, 2869709636, 37213570517, 517042337684, 7662657179226, 120659644766574, 2011723372797539, 35404257343474321, 655872050192283400] "" "Class ", 2288, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 527, 3236, 22514, 174880, 1499310, 14057385, 143044306, 1569697721, 18474714192, 232121928099, 3100650268514, 43875508957201, 655594797322295, 10314589700199580, 170433917547659875] "" "Class ", 2289, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 2290, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 2291, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 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}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 521, 3139, 21309, 160944, 1337966, 12134861, 119220060, 1261163862, 14290091759, 172655370556, 2215633374182, 30093879216394, 431296779214479, 6504120326528368, 102951196745879700] "" "Class ", 2292, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 3}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 474, 2572, 15128, 95480, 641476, 4559456, 34117751, 267690526, 2194878299, 18753162312, 166556017674, 1534408380462, 14635275202556, 144283194442089, 1468035937630809] "" "Class ", 2293, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 2294, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 2295, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 504, 2999, 20081, 149527, 1225319, 10954993, 106113091, 1106962938, 12372612020, 147506134874, 1868427790220, 25058288749475, 354724005167796, 5285526406110554, 82690748997600112] "" "Class ", 2296, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {2, 3}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2616, 16017, 106846, 769203, 5931219, 48687066, 423294291, 3881198633, 37392938198, 377339950091, 3977288011298, 43680286908412, 498745329008570, 5909036239859276] "" "Class ", 2297, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[1, 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}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2942, 19592, 145325, 1187400, 10595217, 102502015, 1068492377, 11938273813, 142320676209, 1803082426768, 24190925738379, 342624247420595, 5108502446210859, 79979884424225795] "" "Class ", 2298, " is:" {{[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 2299, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 2, 4], [1, 0, 0]]} "Class ", 2300, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 0]]} "Class ", 2301, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2914, 19117, 138885, 1106150, 9578360, 89555300, 898853953, 9636632985, 109883386827, 1327630028317, 16940286029456, 227605646402928, 3211574567086222, 47478124191443140] "" "Class ", 2302, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2434, 14306, 91338, 628882, 4641598, 36536590, 305369118, 2699416886, 25151954346, 246268054586, 2526973130226, 27107795270058, 303346590735062, 3534079220213390] "" "Class ", 2303, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2304, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 2305, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2607, 15965, 106703, 771328, 5986695, 49591357, 436214115, 4056919161, 39744777289, 408828535620, 4402898987581, 49518941902847, 580303281315282, 7071392412423459] "" "Class ", 2306, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {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, 6, 22, 93, 438, 2249, 12410, 72836, 451229, 2933452, 19919733, 140763073, 1031951249, 7828464986, 61318432878, 494977125303, 4111002457845, 35079551022272, 307149716827556] "" "Class ", 2307, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 2308, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 2309, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 516, 3123, 21378, 163305, 1376605, 12691840, 127031772, 1371615647, 15890685727, 196613557049, 2587433027080, 36086361542882, 531670868848664, 8251298985467428, 134542595259910342] "" "Class ", 2310, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 488, 2838, 18624, 136272, 1100604, 9729182, 93459888, 969635016, 10807235764, 128802397386, 1634767169344, 22015601734440, 313571783064516, 4709860432790406, 74404619751158592] "" "Class ", 2311, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 2312, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 2313, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2676, 16827, 116531, 880844, 7213525, 63602722, 600588304, 6045885885, 64622952235, 730846912302, 8718057395092, 109383537850254, 1439895035410330, 19841240465990613] "" "Class ", 2314, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2269, 12673, 75772, 481560, 3235247, 22874471, 169585733, 1314257091, 10618739860, 89241155459, 778527244881, 7037404695759, 65807445713268, 635656196569149] "" "Class ", 2315, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 2316, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 2317, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3100, 21143, 160899, 1351326, 12413680, 123806199, 1332147059, 15381153274, 189681166334, 2488186404306, 34593792027366, 508132214201288, 7862696145885716, 127837895873280100] "" "Class ", 2318, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2810, 18322, 133234, 1070126, 9414260, 90057994, 930958238, 10343283702, 122928834458, 1556358375506, 20913412144340, 297283978326242, 4457262013467746, 70300645460855990] "" "Class ", 2319, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 2320, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 2321, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2790, 17903, 126965, 986075, 8324872, 75920825, 743925957, 7795836897, 87013131016, 1030679879049, 12914460498958, 170679369108291, 2373004095748690, 34625315153576903] "" "Class ", 2322, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2443, 14352, 91333, 624640, 4561956, 35391648, 290357898, 2509418819, 22769704890, 216271249710, 2144639780723, 22151496424455, 237808684815655, 2648501674187504] "" "Class ", 2323, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 2324, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 2325, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 526, 3212, 22172, 170629, 1448016, 13431705, 135185900, 1467141045, 17077974492, 212234913062, 2804500266140, 39264550664986, 580593599372196, 9041382507146303, 147902602856907815] "" "Class ", 2326, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2768, 17710, 125327, 971895, 8195707, 74663151, 730729565, 7646174943, 85180767581, 1006559848667, 12575060358348, 165606093984992, 2292927125921682, 33297666463950382] "" "Class ", 2327, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2787, 17832, 125844, 970450, 8116039, 73151233, 706799330, 7287594888, 79865751053, 927060542535, 11362677753803, 146647431203868, 1987948746646179, 28241675423797895] "" "Class ", 2328, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2444, 14373, 91604, 627649, 4593732, 35722914, 293836670, 2546650144, 23178422047, 220889787932, 2198455672455, 22798471411992, 245832105549915, 2751079812990698] "" "Class ", 2329, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2786, 17957, 128528, 1012972, 8727676, 81691038, 826072403, 8980194147, 104485783760, 1296003766293, 17075597958565, 238208870808100, 3508124685628667, 54395812577095576] "" "Class ", 2330, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 2331, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "Class ", 2332, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 2333, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 2985, 19930, 147959, 1208880, 10776825, 104091907, 1082866622, 12070396652, 143518862652, 1813140252463, 24253707203079, 342454160040935, 5089756253132819, 79427856225096423] "" "Class ", 2334, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2532, 15420, 102620, 739512, 5729192, 47429896, 417429800, 3888426512, 38192416048, 394239339792, 4264424937488, 48212317486112, 568395755184224, 6973300915138656] "" "Class ", 2335, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]} "Class ", 2336, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]} "Class ", 2337, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "Class ", 2338, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2298, 12967, 78421, 504442, 3430805, 24554151, 184210671, 1443988074, 11794579296, 100149247378, 882198744660, 8047314804252, 75892620322949, 738892803484753] "" "Class ", 2339, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]} "Class ", 2340, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]} "Class ", 2341, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2939, 19496, 143650, 1163194, 10261879, 97943219, 1005353037, 11041923056, 129191539936, 1604005931154, 21060968111343, 291563666572811, 4244154964400143, 64802078628450244] "" "Class ", 2342, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2598, 15923, 106784, 776662, 6081880, 50967416, 454750348, 4301056798, 42958549822, 451598655332, 4982069092072, 57529048070188, 693696896374292, 8716516562283788] "" "Class ", 2343, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 2344, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 2345, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2573, 15656, 104140, 750586, 5820284, 48261988, 425745944, 3977882455, 39213808934, 406489065469, 4417657070995, 50202264656332, 595140562931186, 7344478415066021] "" "Class ", 2346, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {1, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2249, 12410, 72836, 451229, 2933452, 19919733, 140763073, 1031951249, 7828464986, 61318432878, 494977125303, 4111002457845, 35079551022272, 307149716827556] "" "Class ", 2347, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 2348, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 2349, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 505, 3022, 20373, 152683, 1259200, 11329521, 110399362, 1158000325, 13007242568, 155754868644, 1980452910003, 26646674562740, 378211794210775, 5647284049672213, 88486123753610031] "" "Class ", 2350, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2532, 15420, 102620, 739512, 5729192, 47429896, 417429800, 3888426512, 38192416048, 394239339792, 4264424937488, 48212317486112, 568395755184224, 6973300915138656] "" "Class ", 2351, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 2352, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 2353, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 462, 2574, 16009, 109793, 822640, 6683705, 58509550, 548846022, 5490706356, 58340613456, 656010924274, 7781486508131, 97093834250989, 1271138847618457, 17420901410471800] "" "Class ", 2354, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 2355, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 2356, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 2357, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3121, 21415, 163976, 1385591, 12804731, 128452337, 1389989030, 16137394257, 200068243803, 2637977408426, 36859311106773, 544021364926167, 8457328068080438, 138127180027531060] "" "Class ", 2358, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 488, 2838, 18620, 136200, 1099654, 9717728, 93324378, 968005552, 10786978596, 128539928912, 1631209774200, 21965100617024, 312820860281802, 4698172513584352, 74214384001596254] "" "Class ", 2359, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 2360, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 2361, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2667, 16830, 117623, 902182, 7537156, 68139583, 662862458, 6904898782, 76689578239, 904715500049, 11298414056777, 148915023642816, 2065815783174718, 30088844300975092] "" "Class ", 2362, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3, 5], {2, 3, 4}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2443, 14352, 91333, 624640, 4561956, 35391648, 290357898, 2509418819, 22769704890, 216271249710, 2144639780723, 22151496424455, 237808684815655, 2648501674187504] "" "Class ", 2363, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 2364, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 2365, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3062, 20618, 154293, 1270167, 11405072, 110913714, 1161245365, 13022132600, 155711499096, 1977606426795, 26585026657058, 377115389679477, 5629266665742520, 88204011475506562] "" "Class ", 2366, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2790, 17874, 126260, 974056, 8143110, 73294136, 706384540, 7255499970, 79100654118, 912076499426, 11087998533588, 141718997445238, 1899610606246638, 26642721217362962] "" "Class ", 2367, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 0]]} "Class ", 2368, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 0]]} "Class ", 2369, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "Class ", 2370, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2441, 14293, 90330, 610936, 4392320, 33385893, 267085896, 2240361413, 19641119872, 179468466399, 1705021672838, 16805938640252, 171538472104140, 1810037548263378] "" "Class ", 2371, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [0, 1, 1]]} "Class ", 2372, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 3, 4, 2], [1, 1, 1]]} "Class ", 2373, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3205, 22112, 170081, 1442800, 13379403, 134630547, 1460885297, 17003262701, 211290587708, 2791895604385, 39087274279718, 577972162077987, 9000710529537499, 147241814520302415] "" "Class ", 2374, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 96, 484, 2769, 17722, 125456, 973257, 8210506, 74832285, 732764997, 7671912810, 85521795121, 1011281866759, 12643243270556, 166631075303068, 2308946684854062, 33557660196275548] "" "Class ", 2375, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 2376, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 2377, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2803, 18163, 130777, 1036932, 8985831, 84554732, 859088719, 9377799500, 109499631018, 1362273172808, 17993740869264, 251536396774858, 3710643811991217, 57613942390283874] "" "Class ", 2378, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 2379, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 2380, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 2381, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3190, 21883, 167130, 1405925, 12915292, 128624080, 1380249170, 15875636694, 194833951794, 2541125916784, 35098315885400, 511780741347247, 7855978280435404, 126630159830602276] "" "Class ", 2382, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2948, 19468, 142536, 1145054, 10011760, 94627066, 961201586, 10441276956, 120769417766, 1481764208064, 19220564264696, 262797966217640, 3777325930373024, 56938393801915768] "" "Class ", 2383, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} "Class ", 2384, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} "Class ", 2385, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "Class ", 2386, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2581, 15590, 102193, 720426, 5423381, 43348119, 366112600, 3254256966, 30337698743, 295738012734, 3006674651729, 31806332160940, 349374642791060, 3977541917759969] "" "Class ", 2387, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} "Class ", 2388, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} "Class ", 2389, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3173, 21697, 165053, 1382224, 12632611, 125090148, 1333903614, 15238284330, 185650973550, 2402651689931, 32915542596455, 475860608396305, 7239688631496748, 115620265822296990] "" "Class ", 2390, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {[1, 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, 6, 22, 96, 485, 2788, 17955, 127956, 999321, 8485932, 77837269, 766896633, 8076941771, 90549653899, 1076579403289, 13529976124872, 179211025571010, 2495189020938888, 36431567831715307] "" "Class ", 2391, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 2392, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 2393, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2698, 16804, 114616, 848182, 6759244, 57646974, 523399272, 5036195268, 51154864682, 546645532298, 6127109525068, 71842125840688, 879107674203370, 11202491231064552] "" "Class ", 2394, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 4, 2, 3], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 3, 4, 1], {1, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {1, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 435, 2199, 11848, 67405, 402245, 2505752, 16234286, 109070637, 758102731, 5440417333, 40242866641, 306384315930, 2397788906989, 19267668391506, 158809810987035] "" "Class ", 2395, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 2396, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 2397, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2980, 19930, 148117, 1210149, 10776020, 103842274, 1076424668, 11941483000, 141145635480, 1770608339447, 23492745061649, 328682848615066, 4835786506633477, 74633993701902495] "" "Class ", 2398, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2483, 14868, 97056, 684761, 5185095, 41893424, 359392528, 3259834475, 31148672459, 312545979000, 3283938029756, 36040837059503, 412230564514829, 4904045619272402] "" "Class ", 2399, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2480, 14813, 96368, 677163, 5104425, 41040812, 350275316, 3160362326, 30036193255, 299759321853, 3132691546993, 34198649704191, 389123146828974, 4605606838584411] "" "Class ", 2400, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2144, 11576, 66424, 402246, 2556919, 16987488, 117542228, 844557382, 6285605863, 48351824157, 383719085244, 3136424958232, 26366044853793, 227656007260611] "" "Class ", 2401, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2526, 15471, 104313, 767370, 6114106, 52440456, 481662994, 4716370728, 49040152913, 539596410771, 6263572744908, 76491759794465, 980324197599920, 13155656062116289] "" "Class ", 2402, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 2403, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "Class ", 2404, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 2405, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2923, 19306, 141644, 1142539, 10046434, 95624330, 979382618, 10738458594, 125489819347, 1556902765878, 20436551305929, 282955166380497, 4120981159759561, 62977200700256356] "" "Class ", 2406, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2592, 15936, 107730, 794130, 6339080, 54467319, 501169619, 4916176173, 51210835465, 564527055247, 6565367971931, 80331769934246, 1031551065563052, 13870499389376620] "" "Class ", 2407, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 2408, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 2409, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2582, 15731, 104716, 755092, 5856879, 48580100, 428756217, 4009222354, 39572170819, 410942045086, 4476898265723, 51034240324916, 607339059606098, 7529768643291838] "" "Class ", 2410, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2254, 12528, 74582, 472530, 3169685, 22413943, 166474654, 1294623421, 10512873813, 88929017003, 781967036421, 7133985481105, 67411188066059, 658739589377738] "" "Class ", 2411, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 2412, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 2413, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 526, 3227, 22428, 174030, 1490560, 13962520, 141959899, 1556611943, 18308019879, 229882604792, 3068972089790, 43404397674734, 648242178653655, 10194376742656630, 168378475246092042] "" "Class ", 2414, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2718, 17084, 118152, 891202, 7278373, 63965829, 601782613, 6033149075, 64201904140, 722674433744, 8578067325907, 107075823371063, 1402078406456747, 19215810668460836] "" "Class ", 2415, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 2416, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 2417, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2808, 18282, 132672, 1063122, 9330144, 89045046, 918468480, 10183816854, 120807999360, 1526893903818, 20485349775360, 290780492531490, 4353992234104320, 68588265490962390] "" "Class ", 2418, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 434, 2179, 11600, 64912, 379767, 2314747, 14661845, 96313979, 654957013, 4602598017, 33367894225, 249167486380, 1913539720065, 15092760062939, 122108078017601] "" "Class ", 2419, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 2420, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 2421, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2974, 19956, 149258, 1230597, 11084911, 108291180, 1140262521, 12872365963, 155078417749, 1985788025880, 26931370987175, 385616400748951, 5812940717113051, 92018296864739220] "" "Class ", 2422, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2530, 15590, 106399, 797406, 6514307, 57637368, 549219594, 5608677288, 61117344624, 707927718616, 8686514506494, 112564010634324, 1536201484821799, 22024315733669313] "" "Class ", 2423, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2424, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 2425, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2653, 16661, 115702, 880703, 7293169, 65285152, 628227164, 6467417044, 70928812982, 825603737981, 10165675886155, 132015867602280, 1803348138190976, 25849098270997609] "" "Class ", 2426, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2307, 13168, 81313, 539364, 3820430, 28751857, 228905479, 1920624009, 16927177635, 156245775049, 1506531237205, 15138284519986, 158192949696643, 1715851339793212] "" "Class ", 2427, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 2428, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 2429, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]} "Class ", 2430, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 2431, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}] , [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2096, 11060, 61679, 361681, 2221871, 14256965, 95304930, 662136590, 4770638225, 35574812934, 274075419218, 2178003526429, 17826849078144, 150087039878734] "" "Class ", 2432, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]} "Class ", 2433, " is:" {{[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}} {[[1, 3, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 2434, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2435, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2436, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2437, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 2438, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 2439, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 2440, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 2441, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 2442, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 2443, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 2444, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 2445, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 2446, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 2447, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 2448, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 2449, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 2450, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 2451, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 2452, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 2453, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 2454, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 2455, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 2456, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 2457, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 2458, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} "Class ", 2459, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 2460, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "Class ", 2461, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "Class ", 2462, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 2463, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 2464, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "Class ", 2465, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "Class ", 2466, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 2467, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 2468, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 2469, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 2470, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]} "Class ", 2471, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]} "Class ", 2472, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 2473, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 2474, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "Class ", 2475, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "Class ", 2476, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 2477, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 2478, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 2479, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 2480, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]} "Class ", 2481, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]} "Class ", 2482, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 2483, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 2484, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "Class ", 2485, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "Class ", 2486, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 2487, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 2488, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 2489, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} "Class ", 2490, " is:" {{[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 2491, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 2, 4], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 2, 4], [1, 1, 0]]} "Class ", 2492, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2493, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2494, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2495, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 1]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2150, 11708, 68282, 423948, 2788230, 19341952, 141003552, 1076787624, 8589843716, 71404154928, 617151121998, 5535236798058, 51426766394244, 494145546973656] "" "Class ", 2496, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 2497, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 2498, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 2499, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 2500, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 2501, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 2502, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 2503, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 2504, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 2505, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 2506, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 2507, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 2508, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 2509, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 2510, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 2511, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 2512, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 2513, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 2514, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 2515, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 2516, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "Class ", 2517, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} "Class ", 2518, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "Class ", 2519, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 2520, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "Class ", 2521, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} "Class ", 2522, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "Class ", 2523, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} "Class ", 2524, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]} "Class ", 2525, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]} "Class ", 2526, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]} "Class ", 2527, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]} "Class ", 2528, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "Class ", 2529, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "Class ", 2530, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]} "Class ", 2531, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]} "Class ", 2532, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "Class ", 2533, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "Class ", 2534, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 2535, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 2536, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "Class ", 2537, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "Class ", 2538, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 2539, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 2540, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 2541, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 2542, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 2543, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 2544, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 2545, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 2546, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 2547, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 2548, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]} "Class ", 2549, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]} "Class ", 2550, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 2551, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 2552, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "Class ", 2553, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "Class ", 2554, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 2555, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 2556, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 0]]} "Class ", 2557, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]} "Class ", 2558, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 0]]} "Class ", 2559, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 0]]} "Class ", 2560, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 0, 1]]} "Class ", 2561, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]} "Class ", 2562, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [0, 1, 1]]} "Class ", 2563, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 3, 4, 2], [1, 1, 1]]} "Class ", 2564, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 2565, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 2566, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 2567, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 2568, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 2569, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 2570, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 2571, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 2572, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} "Class ", 2573, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "Class ", 2574, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} "Class ", 2575, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} "Class ", 2576, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "Class ", 2577, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "Class ", 2578, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} "Class ", 2579, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} "Class ", 2580, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]} "Class ", 2581, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]} "Class ", 2582, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 2583, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 2584, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "Class ", 2585, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "Class ", 2586, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 2587, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} "Class ", 2588, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "Class ", 2589, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 2590, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "Class ", 2591, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} "Class ", 2592, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "Class ", 2593, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 2594, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "Class ", 2595, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 2596, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 2597, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 2598, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 2599, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 2600, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 2601, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 2602, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 2603, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 2604, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 2605, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 2606, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 2607, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 2608, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 2609, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 2610, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 2611, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 2612, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2613, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2614, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2615, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 2616, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 2617, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 2618, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 2619, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 2620, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 0]]} "Class ", 2621, " is:" {{[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}} {[[1, 3, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]} "Class ", 2622, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2683, 16480, 109872, 787622, 6026073, 48916739, 419247013, 3778331586, 35681373671, 352044012696, 3619391803380, 38686759681785, 429036109186848, 4927651140857105] "" "Class ", 2623, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2250, 12426, 73013, 452880, 2947354, 20027743, 141532541, 1036743360, 7849965066, 61293251049, 492508378609, 4065294546366, 34416181099282, 298413198893878] "" "Class ", 2624, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2625, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 2626, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2441, 14293, 90330, 610936, 4392320, 33385893, 267085896, 2240361413, 19641119872, 179468466399, 1705021672838, 16805938640252, 171538472104140, 1810037548263378] "" "Class ", 2627, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2108, 11148, 62096, 361680, 2190720, 13739736, 88919968, 592140320, 4047967744, 28351717168, 203104858976, 1486035040064, 11090626172448, 84337068089184] "" "Class ", 2628, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 2629, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 2630, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2692, 16559, 110587, 794248, 6089750, 49552713, 425838265, 3849107289, 36467531721, 361063640467, 3726131020037, 39988068079905, 445361854497659, 5138204183097173] "" "Class ", 2631, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2572, 15527, 101767, 717628, 5405692, 43244468, 365625958, 3253865175, 30374053489, 296506388635, 3018871233107, 31983027976097, 351848382703692, 4011830396627695] "" "Class ", 2632, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 2633, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 2634, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2317, 13202, 80896, 528842, 3665479, 26801239, 205870087, 1655504471, 13895499376, 121424960137, 1102187017573, 10371787758966, 101003056696585, 1016267738355791] "" "Class ", 2635, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2146, 11624, 67146, 411142, 2656052, 18035178, 128318314, 954086192, 7396278762, 59659032142, 499778527628, 4341025729290, 39035256389026, 362878164902216] "" "Class ", 2636, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 2637, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 2638, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 493, 2811, 17664, 120734, 888735, 6991389, 58414176, 515746114, 4791574286, 46675035350, 475239790622, 5044223307912, 55680389584234, 637861356970105, 7569256695120239] "" "Class ", 2639, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2545, 15241, 98970, 690848, 5148067, 40722711, 340345618, 2993430270, 27612342959, 266340384597, 2679431047040, 28049267024334, 304918003096096, 3435794113891726] "" "Class ", 2640, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 2641, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 2642, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2588, 15713, 103741, 738002, 5615595, 45431921, 388852291, 3506162884, 33184212610, 328640320648, 3396316752324, 36537739251620, 408306211871901, 4730465526016739] "" "Class ", 2643, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2285, 12856, 77631, 499550, 3406399, 24501854, 185196468, 1466177110, 12123823416, 104453217908, 935587202671, 8695177235306, 83702799511281, 833251637996702] "" "Class ", 2644, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2165, 11859, 69597, 434794, 2876584, 20068382, 147102044, 1129391080, 9057511918, 75695407892, 657803437814, 5932706331710, 55434949710352, 535798023308036] "" "Class ", 2645, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 2646, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2433, 14274, 90749, 620193, 4526346, 35086053, 287532721, 2481397654, 22474174039, 212989821058, 2106613659106, 21694647293834, 232145105834012, 2576284131201955] "" "Class ", 2647, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2129, 11431, 65274, 394264, 2508993, 16770477, 117445967, 859888323, 6569249344, 52273085985, 432504691084, 3714925102882, 33073826081440, 304758026087421] "" "Class ", 2648, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 4, 5, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 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], {2}, {[0, 0, 0, 0, 0, 1]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2509, 14786, 93873, 636437, 4575499, 34686515, 276008330, 2296491288, 19915161695, 179504593425, 1677626427854, 16222855197461, 162017619783838, 1668319134577463] "" "Class ", 2649, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2220, 12102, 69945, 425472, 2708771, 17968946, 123750823, 882142212, 6492148236, 49220914558, 383708204675, 3070600370488, 25187263829933, 211499101317740] "" "Class ", 2650, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 2651, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 2652, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 435, 2213, 12085, 70260, 431905, 2792283, 18900047, 133436805, 979549725, 7456788821, 58728881483, 477593192875, 4003221664047, 34532843593454, 306143453434128] "" "Class ", 2653, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 407, 1927, 9546, 49138, 261671, 1437163, 8122097, 47144872, 280619477, 1710458627, 10662856184, 67905421138, 441317433427, 2924131556090, 19736016873809] "" "Class ", 2654, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 2655, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 2656, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2163, 11802, 68654, 422514, 2734920, 18534326, 131010280, 962872915, 7338655095, 57871290084, 471255871064, 3955955936165, 34181250515371, 303583845782291] "" "Class ", 2657, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 2658, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 2, 5, 4, 3], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 3, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2688, 16571, 111048, 801244, 6178119, 50601974, 438067599, 3991782328, 38150613135, 381252621040, 3973175393737, 43077573810225, 484889270955494, 5655833993258190] "" "Class ", 2659, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2447, 14423, 92196, 633848, 4655239, 36320982, 299636199, 2603251514, 23737016318, 226474630597, 2255011207253, 23377372292939, 251797443162041, 2812537008545812] "" "Class ", 2660, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 2661, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 2662, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {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]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2313, 13292, 83006, 559202, 4038149, 31082338, 253767909, 2188234742, 19854419817, 188926815389, 1879905670354, 19510069238574, 210696255669967, 2362808483348378] "" "Class ", 2663, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2134, 11540, 66785, 411542, 2688435, 18544768, 134596513, 1024578697, 8156579870, 67733769479, 585378663314, 5254192645923, 48888318970638, 470765314095903] "" "Class ", 2664, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 2665, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 2666, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 94, 455, 2447, 14416, 92046, 631680, 4628292, 36007712, 296094004, 2563471518, 23287910406, 221340089779, 2195294794013, 22668845465108, 243206325625694, 2705969395693420] "" "Class ", 2667, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 2668, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 491, 2781, 17319, 117122, 852080, 6619829, 54595763, 475656057, 4359801865, 41894895747, 420789116009, 4405870084917, 47979216119834, 542289946249914, 6349850692357560] "" "Class ", 2669, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {[1, 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, 6, 22, 94, 453, 2416, 14080, 88815, 601849, 4354457, 33464422, 271971263, 2328630928, 20935007600, 197046388338, 1936675400216, 19830222010075, 211091790936152, 2331661938553268] "" "Class ", 2670, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 2671, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 2672, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 449, 2345, 13205, 79349, 504844, 3380578, 23713711, 173588677, 1321822851, 10442033281, 85379771968, 721133004320, 6280680193868, 56319332291306, 519241349944391] "" "Class ", 2673, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 404, 1870, 8876, 42788, 208286, 1020250, 5017756, 24743653, 122230393, 604506702, 2992003025, 14816686785, 73399796609, 363701140886, 1802472028508] "" "Class ", 2674, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 2675, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [3, 1, 5, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 389, 1727, 7769, 35190, 160038, 729901, 3337045, 15292671, 70250412, 323513403, 1493623083, 6913684024, 32084705297, 149277396827, 696264956073] "" "Class ", 2676, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 0, 1]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2115, 11285, 63859, 380719, 2378855, 15511979, 105193717, 739741570, 5381228451, 40410428082, 312707876465, 2489654602320, 20365552175866, 170953564959784] "" "Class ", 2677, " is:" {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}} {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {3, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 4, 5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 393, 1790, 8403, 40405, 198329, 991813, 5046876, 26109118, 137234313, 732511739, 3968815804, 21818934217, 121667439207, 687908818439, 3942333535641] "" "Class ", 2678, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2679, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2680, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2681, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 2682, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 2683, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 2684, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 2685, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 2686, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 2687, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 2688, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 2689, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 2690, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 2691, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 2692, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 2693, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 2694, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 2695, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 2696, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 2697, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 2698, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 2699, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 2700, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} "Class ", 2701, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 2702, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "Class ", 2703, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "Class ", 2704, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} "Class ", 2705, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} "Class ", 2706, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "Class ", 2707, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "Class ", 2708, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} "Class ", 2709, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "Class ", 2710, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 2711, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 2712, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 2713, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]} "Class ", 2714, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]} "Class ", 2715, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]} "Class ", 2716, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]} "Class ", 2717, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]} "Class ", 2718, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "Class ", 2719, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]} "Class ", 2720, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 2721, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 2722, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "Class ", 2723, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "Class ", 2724, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]} "Class ", 2725, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} "Class ", 2726, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "Class ", 2727, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "Class ", 2728, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} "Class ", 2729, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 2730, " is:" {{[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} "Class ", 2731, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {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}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 543, 3430, 24748, 200843, 1811245, 17968005, 194452312, 2279774719, 28784340743, 389389223359, 5618755619040, 86144044165452, 1398408153736369, 23962036388970768, 432205103332987632] "" "Class ", 2732, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2914, 19117, 138885, 1106150, 9578360, 89555300, 898853953, 9636632985, 109883386827, 1327630028317, 16940286029456, 227605646402928, 3211574567086222, 47478124191443140] "" "Class ", 2733, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2734, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2735, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3}, {}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 3, 4, 5, 2], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 522, 3150, 21438, 162205, 1350721, 12273569, 120824052, 1280885601, 14547411047, 176208601314, 2267384526416, 30886406406185, 444025831461160, 6718029614773910, 106704194757894728] "" "Class ", 2736, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {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, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [ [1, 3, 4, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2613, 15621, 100499, 689760, 5016508, 38456156, 309400201, 2603252463, 22837386312, 208349367672, 1972346077437, 19336046232871, 195970811974815, 2050123807248940] "" "Class ", 2737, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2738, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2739, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 540, 3400, 24440, 197640, 1776160, 17559520, 189390960, 2212925440, 27845956160, 375421780800, 5398902044800, 82493543228800, 1334620928044800, 22791713804358400, 409706091655097600] "" "Class ", 2740, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 492, 2826, 18077, 127503, 982833, 8222787, 74217961, 718950519, 7440288294, 81924159603, 956281163205, 11795009428771, 153279060902479, 2093141754867017, 29965043316443844] "" "Class ", 2741, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2742, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2743, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3}, {}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 3, 4, 5, 2], {2, 3}, {}], [[1, 4, 2, 3, 5], {2}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {2}, {}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 521, 3159, 21606, 164819, 1386117, 12746287, 127191542, 1368985295, 15807173679, 194911941513, 2556104951226, 35524439820559, 521549452319433, 8065776732345395, 131057114208591566] "" "Class ", 2744, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [ [1, 2, 3, 5, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4}, {[0, 1, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2631, 15925, 104412, 734747, 5511717, 43825631, 367676646, 3241935529, 29943674211, 288881632010, 2903750771760, 30343096261970, 328975856790762, 3694043460454030] "" "Class ", 2745, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2746, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2747, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3423, 24694, 200446, 1808192, 17943917, 194264118, 2278400934, 28777456992, 389436585435, 5621462941286, 86216547067372, 1400088345750288, 23999453817787727, 433035682743729270] "" "Class ", 2748, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 507, 3001, 19964, 147595, 1200143, 10646307, 102309605, 1058803371, 11740037086, 138849823677, 1744790109950, 23214456049222, 326023948738989, 4819612741866001, 74810048277293067] "" "Class ", 2749, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2750, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2751, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2876, 18609, 132796, 1035531, 8758075, 79840837, 780408563, 8141778752, 90298837843, 1060903950072, 13162333985767, 171959141755018, 2359641661464291, 33930631349014056] "" "Class ", 2752, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2753, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 1, 2, 3, 5], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2686, 16538, 110705, 798255, 6154895, 50444990, 437313296, 3993368080, 38274833696, 383863607345, 4017536690916, 43775265603480, 495523601339431, 5816245777337711] "" "Class ", 2754, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2755, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 556, 3561, 26095, 215071, 1969585, 19842006, 218058278, 2596122839, 33286029367, 457258292065, 6700237484583, 104315207487805, 1719604855028246, 29922012465166278, 548061538529351998] "" "Class ", 2756, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3141, 21589, 165519, 1400004, 12948750, 129989954, 1407492030, 16349346662, 202791366188, 2674999344705, 37390561660427, 552047840116224, 8584719564266686, 140246606966831956] "" "Class ", 2757, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2758, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2759, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3078, 20810, 156438, 1294056, 11678013, 114150040, 1201289440, 13540468504, 162735745422, 2077240938376, 28063179543185, 400028474614950, 5999941101452855, 94454402485438736] "" "Class ", 2760, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2534, 15007, 95567, 648443, 4656453, 35204542, 279049785, 2310968240, 19937067430, 178728930457, 1661318845041, 15981265202264, 158832580815916, 1628495533673983] "" "Class ", 2761, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2762, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2763, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 540, 3412, 24632, 200232, 1808200, 17963440, 194665680, 2285380912, 28893994784, 391401421920, 5655423507040, 86823506958400, 1411343976438720, 24216401536093504, 437383794665601920] "" "Class ", 2764, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 524, 3213, 22348, 174058, 1499708, 14166071, 145543334, 1615933279, 19279612528, 245991852096, 3342336366110, 48180246497157, 734410676673180, 11802537777960621, 199444743521018736] "" "Class ", 2765, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2766, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2767, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 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, 6, 22, 98, 511, 3061, 20716, 156317, 1301528, 11853086, 117214378, 1250824848, 14326896971, 175317110971, 2282639209194, 31508034084999, 459598664349988, 7064111151394368, 114111526073279234] "" "Class ", 2768, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 491, 2793, 17519, 119649, 880825, 6935395, 58037555, 513514788, 4783190038, 46730802425, 477346641225, 5084093543682, 56323877746954, 647652310692881, 7714953775226617] "" "Class ", 2769, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2770, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2771, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 558, 3591, 26436, 218878, 2013610, 20377710, 224965204, 2690555687, 34653851446, 478216313507, 7039245949631, 110092244854631, 1823101989889415, 31867373756610266, 586351418843277049] "" "Class ", 2772, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3141, 21589, 165519, 1400004, 12948750, 129989954, 1407492030, 16349346662, 202791366188, 2674999344705, 37390561660427, 552047840116224, 8584719564266686, 140246606966831956] "" "Class ", 2773, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2774, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2775, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3080, 20881, 157625, 1310636, 11899767, 117112295, 1241670882, 14107960666, 170998563940, 2202211518185, 30028571417456, 432175137840291, 6546629190373723, 104114928902503527] "" "Class ", 2776, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2777, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2778, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2779, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 495, 2877, 18736, 135144, 1068877, 9194827, 85437696, 852550623, 9090456364, 103126044876, 1240009017814, 15750885877903, 210726383229069, 2961499269007731, 43615683215936926] "" "Class ", 2780, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2781, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2782, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 508, 3029, 20369, 152884, 1265767, 11468071, 112821768, 1198036638, 13655870765, 166325159175, 2155664171049, 29623332782135, 430235482055974, 6584919266435416, 105933216019388409] "" "Class ", 2783, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2631, 15925, 104412, 734747, 5511717, 43825631, 367676646, 3241935529, 29943674211, 288881632010, 2903750771760, 30343096261970, 328975856790762, 3694043460454030] "" "Class ", 2784, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2785, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2786, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3084, 20905, 157705, 1310019, 11878538, 116727307, 1235530358, 14013126566, 169531489187, 2179097698749, 29654684069739, 425938898750463, 6439128202064945, 102197702652067491] "" "Class ", 2787, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2788, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2789, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3119, 21401, 164185, 1393284, 12961998, 131207044, 1435823929, 16892536690, 212638681591, 2851707547295, 40593681667258, 611304011496855, 9709737101319283, 162234899719967947] "" "Class ", 2790, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2702, 16709, 112323, 812910, 6286349, 51630808, 448138697, 4093535708, 39212642137, 392704366492, 4100699948438, 44543233344287, 502261705283887, 5868020629199118] "" "Class ", 2791, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2792, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2793, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 544, 3454, 25070, 204732, 1857734, 18542630, 201904340, 2381669374, 30255334790, 411799436760, 5978583272382, 92223109184208, 1506276910969542, 25968745680808178, 471274044859825078] "" "Class ", 2794, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3044, 20484, 153389, 1264581, 11378507, 110935223, 1164785361, 13102181972, 157179215310, 2002990927609, 27019418954008, 384622981222950, 5761655343704635, 90598923340344464] "" "Class ", 2795, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2796, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2797, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}}, " the pattern set ", {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2916, 19151, 139304, 1110886, 9631143, 90153027, 905834339, 9721322824, 110954409491, 1341764689742, 17134958851610, 230402111996136, 3253435695635378, 48130434728662797] "" "Class ", 2798, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2799, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2800, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2801, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 545, 3460, 25102, 204874, 1858031, 18535912, 201727259, 2378351966, 30197585220, 410801012839, 5961005478160, 91904438231220, 1500296260212174, 25852269181694544, 468917786077086448] "" "Class ", 2802, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 516, 3127, 21441, 163920, 1382796, 12754158, 127686527, 1378738633, 15971619770, 197567678107, 2599091801985, 36232876276866, 533549834978132, 8275526436097450, 134849096682870073] "" "Class ", 2803, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2804, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2805, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2945, 19504, 143512, 1161816, 10264112, 98271790, 1013632350, 11205717347, 132176295876, 1656933604039, 21997540633405, 308322874307913, 4549721824579765, 70504296131022177] "" "Class ", 2806, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2603, 15837, 104510, 741127, 5606925, 44984976, 380896935, 3389901341, 31602121584, 307686442845, 3120627729781, 32895075644601, 359666968077780, 4071636112716798] "" "Class ", 2807, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2808, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2809, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 543, 3445, 24988, 203914, 1848923, 18440584, 200641054, 2364977362, 30020576298, 408295248061, 5923226339466, 91300104092447, 1490073866850869, 25669973467867903, 465499733154622449] "" "Class ", 2810, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2943, 19584, 145096, 1184188, 10552762, 101941191, 1060975195, 11834613832, 140837110570, 1780991373641, 23848334769427, 337089260391572, 5015380469545257, 78349739705120789] "" "Class ", 2811, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2812, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2813, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 1, 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, 6, 22, 98, 515, 3121, 21415, 163976, 1385591, 12804731, 128452337, 1389989030, 16137394257, 200068243803, 2637977408426, 36859311106773, 544021364926167, 8457328068080438, 138127180027531060] "" "Class ", 2814, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3, 5], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2506, 14725, 93065, 627321, 4480528, 33732889, 266581625, 2203617227, 18996910364, 170358684096, 1585687677240, 15289615256108, 152457639546338, 1569648086283162] "" "Class ", 2815, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2816, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2817, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 556, 3571, 26219, 216560, 1987640, 20066778, 221008772, 2636943028, 33882622586, 466462066372, 6849903417166, 106876326442910, 1765640066581540, 30789591828303077, 565173877266880123] "" "Class ", 2818, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3107, 21171, 160715, 1345051, 12304489, 122150878, 1307922414, 15025453630, 184348239606, 2405828459328, 33277762700286, 486323900206978, 7487554247364178, 121137833406358541] "" "Class ", 2819, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {2, 3}, {}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {2, 3}, {}], [[3, 4, 1, 5, 2], {2, 3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3118, 21336, 162660, 1366324, 12532275, 124589141, 1334089939, 15304653700, 187236465145, 2432966694720, 33459543643082, 485483768847313, 7411028751149111, 118722459656618310] "" "Class ", 2820, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {3, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2767, 17485, 120691, 900630, 7207402, 61454003, 555309471, 5293977503, 53043141668, 556728135389, 6103436855126, 69714629882260, 827783563891539, 10197235926168322] "" "Class ", 2821, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3041, 20440, 152772, 1257160, 11291196, 109908180, 1152515298, 12951880402, 155288243540, 1978548607676, 26695640325476, 380248878545162, 5701867083497517, 89783145265371499] "" "Class ", 2822, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2823, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 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], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2708, 16834, 114092, 834929, 6547119, 54672102, 483683075, 4513872015, 44270680992, 454844976600, 4881658965760, 54594453561363, 634813723888265, 7659507432578549] "" "Class ", 2824, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2825, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 557, 3577, 26262, 216917, 1990766, 20097352, 221333590, 2640690058, 33929099364, 467079102701, 6858628388740, 107007210133762, 1767715605715211, 30824273198122154, 565782733301743191] "" "Class ", 2826, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3049, 20483, 152934, 1256709, 11269826, 109533425, 1146906886, 12871238986, 154125350957, 1961423710353, 26435834440182, 376169915853318, 5635456297459811, 88660896725310029] "" "Class ", 2827, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2828, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2829, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 528, 3257, 22803, 178609, 1547309, 14688478, 151618331, 1690739857, 20255139453, 259439755642, 3537967854252, 51177305920885, 782667854382677, 12617579054054375, 213857044795291524] "" "Class ", 2830, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2702, 16709, 112323, 812910, 6286349, 51630808, 448138697, 4093535708, 39212642137, 392704366492, 4100699948438, 44543233344287, 502261705283887, 5868020629199118] "" "Class ", 2831, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2832, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]} "Class ", 2833, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 544, 3444, 24914, 202746, 1833218, 18233408, 197837504, 2325470714, 29437274706, 399252287398, 5775983124318, 88783724505302, 1444988498010816, 24824271767591372, 448915953141309994] "" "Class ", 2834, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 522, 3150, 21446, 162445, 1354659, 12330885, 121625165, 1292039267, 14705683030, 178518374531, 2302236435295, 31431648543098, 452879999065090, 6867333136424771, 109318115289007916] "" "Class ", 2835, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2836, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2837, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 2, 3, 5], {1, 2}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2916, 19151, 139304, 1110886, 9631143, 90153027, 905834339, 9721322824, 110954409491, 1341764689742, 17134958851610, 230402111996136, 3253435695635378, 48130434728662797] "" "Class ", 2838, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 475, 2599, 15466, 98965, 675188, 4879183, 37151738, 296811792, 2479310437, 21589617298, 195489539982, 1836586981958, 17867746659690, 179702462074333, 1865513150455527] "" "Class ", 2839, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2840, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 0]]} "Class ", 2841, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 504, 3010, 20308, 152766, 1268327, 11519759, 113632968, 1209722343, 13825065954, 168814797705, 2193506836094, 30218612482238, 439964147131589, 6750098491445977, 108848526234318634] "" "Class ", 2842, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2843, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 2844, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}], [[4, 1, 2, 3, 5], {1, 2}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {2, 3}, {}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 504, 3012, 20306, 152368, 1258930, 11353752, 110951320, 1167668451, 13165066334, 158295975298, 2021782297329, 27333493166588, 389941872382766, 5853807904074647, 92240461632623277] "" "Class ", 2845, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 2}, {}], [[5, 1, 2, 3, 4], {2}, {}], [[5, 1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2603, 15837, 104510, 741127, 5606925, 44984976, 380896935, 3389901341, 31602121584, 307686442845, 3120627729781, 32895075644601, 359666968077780, 4071636112716798] "" "Class ", 2846, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 2847, " is:" {{[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 4, 3, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 2848, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 3, 4, 2], [0, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2849, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 554, 3308, 22025, 161699, 1297411, 11294448, 106028267, 1067787891, 11484008098, 131379189296, 1593162750162, 20414248118955, 275627906566013, 3911324164292558, 58201030034375451] "" "Class ", 2850, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[4, 2, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2851, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2920, 19296, 142036, 1153642, 10254331, 99041383, 1033049876, 11574037480, 138632411848, 1767921102731, 23915924392505, 342073513584312, 5158089105844214, 81780610832164055] "" "Class ", 2852, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2434, 14306, 91338, 628882, 4641598, 36536590, 305369118, 2699416886, 25151954346, 246268054586, 2526973130226, 27107795270058, 303346590735062, 3534079220213390] "" "Class ", 2853, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2854, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2855, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2728, 17187, 119248, 903891, 7435680, 66009027, 629303553, 6415538967, 69673678762, 803311823941, 9802504798990, 126243074659762, 1711520051069896, 24369117148238544] "" "Class ", 2856, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {[0, 0, 1, 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]}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2233, 12225, 70955, 433205, 2765501, 18372536, 126538279, 900678596, 6608068215, 49862196675, 386218603617, 3065791381859, 24904158746628, 206760206185056] "" "Class ", 2857, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2858, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2859, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 495, 2880, 18813, 136545, 1090857, 9518340, 90091698, 919537588, 10068464805, 117731643480, 1464261273971, 19301722138033, 268811929127496, 3944031032703374, 60807406795739447] "" "Class ", 2860, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2336, 13104, 78288, 493896, 3270472, 22615464, 162670152, 1212975904, 9350571488, 74340383776, 608312875552, 5114065847104, 44102540457408, 389595453153216] "" "Class ", 2861, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2862, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2863, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 490, 2803, 17805, 124603, 950394, 7855749, 69879128, 666026125, 6767937131, 73071458513, 835083146488, 10073756860196, 127892745359480, 1704879458282608, 23806368355683107] "" "Class ", 2864, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2336, 13104, 78288, 493896, 3270472, 22615464, 162670152, 1212975904, 9350571488, 74340383776, 608312875552, 5114065847104, 44102540457408, 389595453153216] "" "Class ", 2865, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2866, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2867, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2883, 18751, 134961, 1065152, 9149434, 84993441, 849197627, 9082048190, 103533237085, 1253345198900, 16058513938341, 217110518537588, 3089030898550135, 46138650474021140] "" "Class ", 2868, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2519, 14965, 96349, 666787, 4930102, 38746066, 322317606, 2827863072, 26085577459, 252300631911, 2552420770323, 26949390444641, 296377488154566, 3388868121213252] "" "Class ", 2869, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2584, 15762, 105128, 760192, 5919617, 49357126, 438544170, 4135081108, 41229024106, 433306004621, 4786757473306, 55443750178579, 671812131183846, 8498427497979213] "" "Class ", 2870, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2241, 12370, 72814, 453658, 2974586, 20428853, 146384939, 1090803125, 8428970402, 67378139133, 555975279994, 4726786870516, 41335718371508, 371264945684184] "" "Class ", 2871, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2872, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2873, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2874, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2875, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3060, 20641, 155027, 1283512, 11616238, 114096365, 1208884718, 13743915839, 166898514886, 2156039939832, 29523570783927, 427172780920174, 6512058274908023, 104325979198876844] "" "Class ", 2876, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2683, 17002, 119329, 919125, 7710155, 69980273, 683378819, 7144855430, 79635236150, 942643810033, 11810103726784, 156138717168558, 2172384043894927, 31729469457700470] "" "Class ", 2877, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2878, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2879, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2880, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2881, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2882, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2883, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3195, 22112, 171249, 1466740, 13771140, 140635204, 1552182037, 18411389822, 233581883564, 3156199138386, 45252935161375, 686195631331590, 10971912601088372, 184498357240309414] "" "Class ", 2884, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3058, 20750, 157506, 1322686, 12183122, 122146926, 1324518754, 15447439646, 192831941490, 2565512387278, 36241715197058, 541784844462462, 8545264289709202, 141817846453739822] "" "Class ", 2885, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2886, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2887, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2888, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 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, 6, 22, 96, 480, 2692, 16648, 112116, 814224, 6327452, 52287096, 457075564, 4208411336, 40660761004, 410935282520, 4332164340524, 47523612573704, 541311900619660, 6389709611496920] "" "Class ", 2889, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2890, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2891, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3095, 21084, 160281, 1345520, 12363963, 123435349, 1330468351, 15398907217, 190479358385, 2507748378373, 35011593310758, 516679288669603, 8036152308125457, 131387967377290972] "" "Class ", 2892, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2683, 17002, 119329, 919125, 7710155, 69980273, 683378819, 7144855430, 79635236150, 942643810033, 11810103726784, 156138717168558, 2172384043894927, 31729469457700470] "" "Class ", 2893, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2894, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2895, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2896, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2897, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2898, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2899, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2555, 15444, 101968, 729466, 5617432, 46297418, 406360078, 3781925114, 37180802682, 384841460948, 4181440961086, 47568014197488, 565238902269108, 7001002074169322] "" "Class ", 2900, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2901, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2902, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2903, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2904, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2905, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2673, 16911, 118491, 911169, 7630892, 69148096, 674166762, 7037341301, 78313925888, 925571447250, 11578573392723, 152848737200594, 2123483916240932, 30970463688170921] "" "Class ", 2906, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2907, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2908, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2909, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2910, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2911, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2931, 19368, 142269, 1150767, 10166281, 97414567, 1006396030, 11151765405, 131940460402, 1660114887171, 22135377924810, 311783301067822, 4625991778105486, 72116079298693114] "" "Class ", 2912, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 95, 468, 2579, 15680, 104060, 747566, 5773800, 47668417, 418632345, 3894352290, 38233195926, 394861003025, 4277618512415, 48484680145960, 573662226383392, 7070645926143513] "" "Class ", 2913, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2914, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2915, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2916, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2917, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2918, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2919, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2946, 19525, 143811, 1165592, 10310893, 98864155, 1021421884, 11312791284, 133717553137, 1680152382562, 22363093725935, 314327538787502, 4652465660669768, 72332822419439444] "" "Class ", 2920, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2635, 16419, 112751, 846018, 6886230, 60433245, 568815423, 5715890118, 61075517281, 691481547453, 8268923873611, 104145793473794, 1377995515025179, 19110047149233282] "" "Class ", 2921, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2922, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2923, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2924, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2925, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2926, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2927, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2922, 19327, 142320, 1155147, 10246803, 98628599, 1023826056, 11401704550, 135594665721, 1715127448162, 22992380851225, 325631417855008, 4858327780895675, 76164085947053868] "" "Class ", 2928, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[1, 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, 6, 22, 94, 456, 2469, 14738, 96063, 678318, 5154429, 41910013, 362829834, 3330209840, 32284287888, 329476095004, 3529354355704, 39579374606296, 463581151214710, 5659093061738692] "" "Class ", 2929, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2930, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2931, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2932, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2933, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2934, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2935, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3206, 22153, 170921, 1456941, 13598784, 137960040, 1511638639, 17791885508, 223881314060, 2999385157263, 42625607527446, 640491806991463, 10145885530961279, 168987503761815183] "" "Class ", 2936, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 487, 2811, 18196, 130508, 1027090, 8799108, 81508897, 811761913, 8649141285, 98168970513, 1182482067381, 15065424301373, 202412586445743, 2860207966285675, 42404173708257157] "" "Class ", 2937, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 3, 1, 5, 4], {2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 5, 3], {2, 3}, {}], [[2, 5, 1, 3, 4], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {2, 3}, {}], [[3, 4, 1, 5, 2], {2, 3}, {}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3}, {}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 487, 2821, 18385, 133188, 1061928, 9242182, 87195369, 886513977, 9663544370, 112438291259, 1390971195975, 18232172377708, 252420969146734, 3680993628854832, 56397403843529215] "" "Class ", 2938, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 459, 2519, 15310, 101800, 733238, 5675068, 46886927, 411236527, 3811258653, 37175256833, 380325862976, 4068858002794, 45400349469457, 527109864879681, 6354667028459370] "" "Class ", 2939, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2940, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2941, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2942, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2943, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 518, 3158, 21838, 168880, 1444831, 13549280, 138226975, 1524128900, 18063124209, 228984361893, 3091901008913, 44302719185316, 671397444063317, 10729617230551457, 180336749531738451] "" "Class ", 2944, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2669, 16864, 117958, 905514, 7570119, 68475096, 666430310, 6944453683, 77148030318, 910263619281, 11368406105557, 149834103377277, 2078350934837043, 30266037357931054] "" "Class ", 2945, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2946, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2947, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 489, 2859, 18944, 140533, 1155561, 10437980, 102795171, 1096443518, 12594680984, 155026449813, 2035838562622, 28412983858259, 419982400957075, 6554610281402786, 107710947535093907] "" "Class ", 2948, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 443, 2345, 13641, 86385, 590812, 4334225, 33905742, 281403704, 2466983263, 22756798975, 220139983966, 2226575912530, 23484560868103, 257700284194789, 2935779203407885] "" "Class ", 2949, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2950, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2951, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2952, 19587, 144552, 1174934, 10432474, 100484353, 1043612748, 11626495655, 138309572934, 1749893094558, 23463137146779, 332354415298477, 4959342612716685, 77757282023313230] "" "Class ", 2952, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 487, 2803, 18074, 129118, 1011919, 8634367, 79681398, 790742224, 8397322942, 95017484139, 1141235928132, 14501000494469, 194341473837513, 2739714335548792, 40528263752079317] "" "Class ", 2953, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2954, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2955, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2464, 14639, 94674, 661251, 4955504, 39628529, 336573933, 3023662907, 28629915425, 284827214283, 2969035375772, 32348279692696, 367561118030057, 4346959242858904] "" "Class ", 2956, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2290, 12956, 78954, 514395, 3560737, 26052263, 200591244, 1619290769, 13661533638, 120125859671, 1098214917149, 10416626691162, 102313704394065, 1038895334226183] "" "Class ", 2957, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2958, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}, {[[3, 1, 2, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 0]]} "Class ", 2959, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2960, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 2961, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {2}, {}], [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2540, 15614, 105689, 780325, 6234891, 53551642, 491616499, 4800152207, 49637723887, 541608913477, 6215291780910, 74797429507125, 941555566491350, 12369153955026659] "" "Class ", 2962, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2148, 11647, 67275, 410843, 2636849, 17699199, 123746381, 898155393, 6747868807, 52349013907, 418457779333, 3440216859604, 29040046554184, 251334398109988] "" "Class ", 2963, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]} "Class ", 2964, " is:" {{[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 4, 3, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 2965, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 0]]} {[[2, 4, 3, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2966, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[4, 2, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 3, 4, 2], [1, 0, 1]]} {[[2, 4, 3, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 2967, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2968, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2969, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2970, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2971, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2972, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2973, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2974, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2975, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2976, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2977, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2978, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2979, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2980, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2981, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2982, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 2983, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2984, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2985, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2986, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2987, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2988, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2989, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2990, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2991, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2992, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2993, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2994, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2995, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2996, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2997, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2998, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 2999, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3000, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3001, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3002, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3003, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3004, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3005, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3006, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3007, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3008, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3009, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3010, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3011, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3012, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3013, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3014, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3015, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3016, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3017, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3018, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3019, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3020, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3021, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3022, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3023, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3024, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3025, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3026, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3027, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3028, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3029, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3030, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3031, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3032, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3033, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3034, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3035, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3036, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3037, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3038, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3039, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3040, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3041, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3042, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3043, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3044, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3045, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3046, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3047, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3048, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3049, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3050, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3051, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3052, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3053, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3054, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3055, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3056, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3057, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3058, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3059, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3060, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3061, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3062, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3063, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3064, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3065, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3066, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3067, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3068, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3069, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3070, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3071, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3072, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 0]]} "Class ", 3073, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]} {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3074, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]} {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]} "Class ", 3075, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]} {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3076, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3077, " is:" {{[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 4, 3, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3078, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 0]]} {[[2, 4, 3, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3079, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 3, 4, 2], [1, 0, 1]]} {[[2, 4, 3, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3080, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[4, 2, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3081, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3082, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3083, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3084, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3085, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3086, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3087, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3088, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3089, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3090, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3091, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3092, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3093, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3094, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3095, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3096, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3097, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3098, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3099, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3100, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3101, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3102, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3103, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3104, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3105, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3106, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3107, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3108, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3109, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3110, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3111, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3112, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3113, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3114, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3115, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3116, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3117, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3118, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3119, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3120, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3121, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3122, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3123, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3124, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3125, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3126, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3127, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3128, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3129, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3130, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3131, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3132, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3133, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3134, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3135, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3136, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3137, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3138, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3139, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3140, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3141, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3142, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3143, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3144, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3145, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3146, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3147, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3148, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3149, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3150, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3151, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3152, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3153, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3154, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3155, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3156, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3157, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3158, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3159, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3160, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3161, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3162, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3163, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3164, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3165, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3166, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3167, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3168, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3169, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3170, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3171, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3172, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3173, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3174, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 396, 1846, 9058, 46660, 252146, 1429734, 8511604, 53229126, 349736370, 2413385356, 17474189146, 132561472342, 1051682980460, 8707567860654, 75078289720450] "" "Class ", 3175, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3176, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {4}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {5}, {[0, 0, 0, 0, 1, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [ [3, 1, 4, 2, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 367, 1565, 6759, 29414, 128611, 564053, 2478756, 10907901, 48046664, 211778564, 933937458, 4120173785, 18181775463, 80251283286, 354276210571] "" "Class ", 3177, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3178, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3179, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3180, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3181, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3182, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 393, 1789, 8375, 39986, 193675, 948309, 4682581, 23277506, 116349290, 584205975, 2944681326, 14891696201, 75526042009, 384012878243, 1956900565819] "" "Class ", 3183, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]} "Class ", 3184, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}, {[[3, 1, 2, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 1, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 1, 4, 3, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 5, 4, 2], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 378, 1646, 7264, 32298, 144236, 645832, 2896554, 13004777, 58428634, 262633878, 1180901976, 5310957342, 23889072924, 107466711108, 483485442636] "" "Class ", 3185, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]} {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3186, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 2, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 379, 1664, 7466, 34092, 158105, 743819, 3547688, 17149454, 84014800, 417169511, 2100055263, 10721727914, 55539353752, 292040996556, 1559571790287] "" "Class ", 3187, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]} "Class ", 3188, " is:" {{[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 4, 3, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3189, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3}, {}], [[1, 5, 3, 2, 4], {2, 3}, {}], [[1, 5, 4, 2, 3], {2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3076, 20791, 156330, 1294085, 11693084, 114506352, 1207913206, 13654959332, 164676919358, 2110298849856, 28635505948277, 410168841935585, 6184506226917495, 97912722397668620] "" "Class ", 3190, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2607, 15965, 106703, 771328, 5986695, 49591357, 436214115, 4056919161, 39744777289, 408828535620, 4402898987581, 49518941902847, 580303281315282, 7071392412423459] "" "Class ", 3191, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3192, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3193, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2922, 19181, 139399, 1110463, 9618591, 89981338, 903950789, 9704239308, 110854741506, 1342462245935, 17177960947712, 231571784628075, 3280186932258714, 48705386018405462] "" "Class ", 3194, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2424, 14090, 88184, 589300, 4177440, 31248612, 245599126, 2020850594, 17354981328, 155150221730, 1440528577804, 13862922749170, 138029364200948, 1419625997273008] "" "Class ", 3195, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3196, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3197, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2916, 19171, 139707, 1117585, 9734047, 91688655, 928631541, 10062738931, 116160200754, 1423039627873, 18438875298508, 251945483109156, 3620458067927262, 54581962245057661] "" "Class ", 3198, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3199, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3200, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3201, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2730, 17172, 118520, 889116, 7194004, 62383568, 576677816, 5656891176, 58653066696, 640584346608, 7347121283680, 88255946135376, 1107672668696048, 14493714457542656] "" "Class ", 3202, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 464, 2511, 14814, 94224, 640544, 4623015, 35232159, 282270209, 2368591365, 20751308498, 189300733507, 1793842203203, 17621328395632, 179107898763397, 1880600989964981] "" "Class ", 3203, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3204, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3205, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {2, 3}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2963, 19732, 146012, 1188023, 10537784, 101174057, 1045143660, 11556754697, 136180217942, 1703400650231, 22539763868745, 314544542032353, 4616627036982970, 71089442283685115] "" "Class ", 3206, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2602, 16011, 108187, 796282, 6341207, 54325383, 498205878, 4869791910, 50541674275, 555077855681, 6431419452322, 78401633900342, 1003089321560073, 13439397812738613] "" "Class ", 3207, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {}, {}], [[3, 1, 4, 2, 5], {2, 3}, {}], [[3, 1, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 1, 5], {2, 3}, {}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {}], [[4, 2, 5, 1, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}], [[4, 3, 5, 1, 2], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 3, 5, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2611, 16043, 107767, 784291, 6138924, 51370470, 457231912, 4309994970, 42865104292, 448324449645, 4916822477170, 56397687868395, 675025906687609, 8413148522980980] "" "Class ", 3208, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3209, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2447, 14417, 92081, 632359, 4638757, 36152123, 297979867, 2587483278, 23591245412, 225183136976, 2244459516068, 23306783682451, 251626128107989, 2819217623825697] "" "Class ", 3210, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3211, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2284, 12830, 77224, 494396, 3347493, 23862051, 178408207, 1394690634, 11369258136, 96419859753, 848968827638, 7746704898169, 73136185670541, 713337693063597] "" "Class ", 3212, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3213, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3111, 21257, 162097, 1364308, 12561123, 125568922, 1354336924, 15675120913, 193775239538, 2548046609221, 35511310501830, 522853060929706, 8109548685773490, 132157919869976957] "" "Class ", 3214, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 476, 2720, 17484, 125078, 986851, 8520984, 79982509, 811384415, 8850017719, 103314602054, 1285613611394, 16990562694461, 237701308580554, 3509932860696945, 54556578047120990] "" "Class ", 3215, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3216, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3217, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2662, 16686, 115175, 867526, 7077593, 62151948, 584364452, 5855814704, 62292662096, 700991923970, 8318954180219, 103824848580541, 1359345601920159, 18628487602458003] "" "Class ", 3218, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2145, 11600, 66763, 406031, 2594373, 17335196, 120668399, 872296585, 6531355582, 50541296538, 403424319277, 3316075340303, 28028020211227, 243273999750253] "" "Class ", 3219, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3220, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3221, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {2, 3}, {}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3069, 20847, 158106, 1323833, 12128815, 120679071, 1295768198, 14932961023, 183842763635, 2407921213563, 33431567597790, 490443030733545, 7580255861654275, 123115870682943227] "" "Class ", 3222, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[1, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 495, 2876, 18717, 134902, 1066390, 9173354, 85302718, 852637416, 9116074594, 103810412606, 1254389502020, 16030071996186, 216001918564836, 3060816005629668, 45501385026437748] "" "Class ", 3223, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3224, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3225, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2808, 18282, 132672, 1063122, 9330144, 89045046, 918468480, 10183816854, 120807999360, 1526893903818, 20485349775360, 290780492531490, 4353992234104320, 68588265490962390] "" "Class ", 3226, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2573, 15546, 102035, 720952, 5444530, 43687368, 370651143, 3311236902, 31037719704, 304318706696, 3112704807751, 33134900207920, 366314130919462, 4197778417464450] "" "Class ", 3227, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3228, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3229, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3138, 21537, 164897, 1392979, 12868441, 129040870, 1395779748, 16197878917, 200736059145, 2645736053659, 36953701428381, 545217276855283, 8473006612828195, 138338138699691179] "" "Class ", 3230, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 476, 2720, 17484, 125078, 986851, 8520984, 79982509, 811384415, 8850017719, 103314602054, 1285613611394, 16990562694461, 237701308580554, 3509932860696945, 54556578047120990] "" "Class ", 3231, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3232, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3233, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2677, 16882, 117635, 897556, 7443533, 66677068, 641657256, 6602661371, 72349589292, 841142376503, 10342058852082, 134085579105283, 1828319634438449, 26156607138196532] "" "Class ", 3234, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3235, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3236, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3237, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3238, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2253, 12494, 74028, 465587, 3092772, 21613111, 158378276, 1213627034, 9701635784, 80732967704, 698024401913, 6259584764544, 58127186865440, 558122327152597] "" "Class ", 3239, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3240, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3241, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2303, 13077, 80004, 523694, 3647688, 26914539, 209578469, 1716656984, 14748812715, 132575174363, 1243952193864, 12158443358085, 123554829786307, 1303141143342983] "" "Class ", 3242, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3243, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2980, 19931, 148180, 1211894, 10810380, 104428128, 1085864189, 12091364577, 143540795704, 1809567415495, 24141897641292, 339804259505926, 5032108034230214, 78208896124902899] "" "Class ", 3244, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2647, 16519, 113454, 850054, 6898066, 60258856, 563722000, 5622112409, 59540032504, 667235401405, 7887913350280, 98096050697895, 1280148489249705, 17490593093429348] "" "Class ", 3245, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3246, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3247, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}}, " the pattern set ", {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2466, 14664, 94872, 662216, 4953040, 39472436, 333571494, 2977000994, 27959177192, 275472505828, 2839566381350, 30548419963360, 342248998839068, 3985291104400310] "" "Class ", 3248, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3249, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3250, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3251, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3}, {}], [[1, 5, 4, 2, 3], {2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2967, 19789, 146722, 1196308, 10633704, 102306926, 1058945657, 11731446389, 138483688512, 1735082070830, 22994350860010, 321346406706242, 4722676815630847, 72810703356408670] "" "Class ", 3252, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 472, 2649, 16544, 113643, 850312, 6876052, 59699230, 553430219, 5452059823, 56843430032, 624978363007, 7223438000143, 87518724482532, 1108791792291378, 14655992773675515] "" "Class ", 3253, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3254, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3255, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2507, 15236, 101850, 742916, 5872476, 50004666, 456301984, 4441978991, 45946567128, 503214155625, 5817214390059, 70781717564670, 904218312109166, 12099790627893338] "" "Class ", 3256, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2179, 11992, 70659, 442357, 2924577, 20318260, 147726792, 1120152670, 8831932357, 72224796934, 611229130698, 5342715540124, 48151695134487, 446771976870560] "" "Class ", 3257, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3258, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3259, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2, 3}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3092, 21097, 160695, 1351325, 12432182, 124191459, 1338555234, 15481892887, 191256236827, 2513207895385, 35001827141546, 514998511447782, 7982243382168101, 129994059131066795] "" "Class ", 3260, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2618, 16211, 110445, 820958, 6610767, 57321640, 532433796, 5273908341, 55488138946, 617942974969, 7261462266689, 89787292258199, 1165275145049374, 15837103429283736] "" "Class ", 3261, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3262, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3263, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 488, 2838, 18620, 136200, 1099654, 9717728, 93324378, 968005552, 10786978596, 128539928912, 1631209774200, 21965100617024, 312820860281802, 4698172513584352, 74214384001596254] "" "Class ", 3264, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}] , [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2270, 12694, 76055, 484743, 3268099, 23199902, 172755852, 1345060127, 10919921160, 92221136963, 808472924744, 7343761349002, 69003158272743, 669680011781166] "" "Class ", 3265, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3266, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3267, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3115, 21307, 162557, 1368223, 12592583, 125797352, 1355543436, 15671611183, 193488045389, 2540785719370, 35358624783016, 519814701891850, 8049803887986086, 130974503883018119] "" "Class ", 3268, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2689, 17136, 121477, 949894, 8133069, 75755158, 763205364, 8273831372, 96074683870, 1190024779582, 15665233531397, 218423706308134, 3216121861543883, 49870692996045560] "" "Class ", 3269, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[1, 0, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {[1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2682, 16971, 118766, 910715, 7593235, 68389547, 661667121, 6843401157, 75343907085, 879726106546, 10857545717938, 141226277508480, 1930829320266853, 27680441196706076] "" "Class ", 3270, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3271, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[1, 0, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2635, 16445, 113351, 855765, 7026519, 62356997, 594905149, 6072584488, 66046481886, 762551699073, 9315334122320, 120046740320560, 1627663553602169, 23162714545186732] "" "Class ", 3272, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3273, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[1, 0, 0, 0]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[1, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [ [2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2320, 13289, 82339, 547984, 3894728, 29418669, 235172266, 1982342327, 17563067869, 163081950770, 1582998620171, 16025849635546, 168857404483332, 1848219057603744] "" "Class ", 3274, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3275, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3111, 21210, 161053, 1347420, 12312797, 122006473, 1302919391, 14916771457, 182251666953, 2366847886054, 32556438917294, 472830746483527, 7230257257840575, 116112531841839380] "" "Class ", 3276, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2636, 16435, 112999, 849786, 6942062, 61239990, 580386371, 5882640913, 63512777908, 727836201036, 8824685916052, 112876460694830, 1519180079904709, 21462592004475590] "" "Class ", 3277, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3278, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3279, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2804, 18146, 130194, 1025466, 8795737, 81601836, 814137470, 8691685642, 98863700941, 1193552809679, 15242371638856, 205287172381499, 2908006251629847, 43220834598072863] "" "Class ", 3280, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2303, 13077, 80004, 523694, 3647688, 26914539, 209578469, 1716656984, 14748812715, 132575174363, 1243952193864, 12158443358085, 123554829786307, 1303141143342983] "" "Class ", 3281, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3282, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]} "Class ", 3283, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {1}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {2, 3}, {}], [[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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2975, 19856, 147385, 1204040, 10733378, 103674143, 1078541877, 12022413164, 142950729136, 1805981490485, 24158013665041, 341101576358118, 5069599054688021, 79111963182623469] "" "Class ", 3284, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2755, 17471, 122126, 932651, 7726480, 69026653, 661590693, 6772842884, 73768628306, 851901287882, 10398765559410, 133795615153049, 1809987606026605, 25685451456577931] "" "Class ", 3285, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3286, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3287, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[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, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2466, 14664, 94872, 662216, 4953040, 39472436, 333571494, 2977000994, 27959177192, 275472505828, 2839566381350, 30548419963360, 342248998839068, 3985291104400310] "" "Class ", 3288, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[1, 4, 2, 3, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 5, 2, 3, 4], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 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, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2231, 12198, 70758, 432683, 2776285, 18627420, 130336134, 948983218, 7177153018, 56296116598, 457353759565, 3843695260631, 33380171631580, 299243766327086] "" "Class ", 3289, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3290, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, {[[3, 1, 2, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 0, 1]]} "Class ", 3291, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1}, {}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 2, 3, 5], {1, 3}, {}], [[5, 1, 2, 3, 4], {3}, {}], [[5, 1, 2, 4, 3], {1, 3}, {[0, 0, 0, 0, 1, 0]}], [[5, 1, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2179, 11992, 70659, 442357, 2924577, 20318260, 147726792, 1120152670, 8831932357, 72224796934, 611229130698, 5342715540124, 48151695134487, 446771976870560] "" "Class ", 3292, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3293, " is:" {{[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 4, 3, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3294, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[4, 2, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 3, 4, 2], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3295, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 479, 2668, 16334, 108590, 776846, 5937492, 48200625, 413600025, 3736037799, 35401749834, 350835409895, 3626545529825, 39009792286722, 435748642897613, 5045045772327322] "" "Class ", 3296, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2249, 12410, 72836, 451229, 2933452, 19919733, 140763073, 1031951249, 7828464986, 61318432878, 494977125303, 4111002457845, 35079551022272, 307149716827556] "" "Class ", 3297, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3298, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3299, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2553, 15292, 99233, 691632, 5142487, 40565057, 337925699, 2961412681, 27210841334, 261394120931, 2618533655490, 27293009418886, 295394053393594, 3313771903807877] "" "Class ", 3300, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2108, 11148, 62096, 361680, 2190720, 13739736, 88919968, 592140320, 4047967744, 28351717168, 203104858976, 1486035040064, 11090626172448, 84337068089184] "" "Class ", 3301, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3302, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3303, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2492, 14574, 91544, 612258, 4330278, 32211795, 250895245, 2038622810, 17226019243, 150962216287, 1368909554516, 12817943135192, 123713438571246, 1228781053005792] "" "Class ", 3304, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2336, 13104, 78288, 493896, 3270472, 22615464, 162670152, 1212975904, 9350571488, 74340383776, 608312875552, 5114065847104, 44102540457408, 389595453153216] "" "Class ", 3305, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3306, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3307, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2492, 14574, 91544, 612258, 4330278, 32211795, 250895245, 2038622810, 17226019243, 150962216287, 1368909554516, 12817943135192, 123713438571246, 1228781053005792] "" "Class ", 3308, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 448, 2336, 13104, 78288, 493896, 3270472, 22615464, 162670152, 1212975904, 9350571488, 74340383776, 608312875552, 5114065847104, 44102540457408, 389595453153216] "" "Class ", 3309, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3310, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3311, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2536, 15070, 96637, 662771, 4827394, 37131319, 300216859, 2541653332, 22457353114, 206507447367, 1971430315301, 19496607777935, 199360375436145, 2104167235840654] "" "Class ", 3312, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2220, 12102, 69949, 425630, 2711940, 18017916, 124407633, 890248804, 6587161558, 50298951150, 395696146420, 3202348942963, 26626613967609, 227196273404042] "" "Class ", 3313, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2249, 12411, 72842, 451172, 2931277, 19880904, 140208708, 1024848435, 7742802004, 60321547124, 483618447539, 3983101713421, 33647425210773, 291134687257293] "" "Class ", 3314, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 409, 1953, 9769, 50694, 271036, 1485404, 8312334, 47353061, 273952590, 1606426544, 9532616265, 57168143536, 346101782300, 2113253909081, 13003104588261] "" "Class ", 3315, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3316, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3317, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {1, 3}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 1993, 10264, 55699, 316564, 1875246, 11532580, 73392005, 481985564, 3258886275, 22640350337, 161331632086, 1177378229857, 8787957205916, 67006297739283] "" "Class ", 3318, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 380, 1679, 7601, 35053, 164049, 777076, 3718289, 17945684, 87257095, 427024641, 2101743074, 10396846080, 51663611964, 257768998470, 1290832017762] "" "Class ", 3319, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2678, 16416, 109216, 781229, 5964805, 48327761, 413508209, 3721378369, 35104337515, 346070131926, 3556203602949, 38004430622817, 421524560509062, 4843513456257911] "" "Class ", 3320, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2321, 13304, 82517, 550000, 3917026, 29662646, 237838239, 2011610430, 17887297644, 166718080190, 1624375571901, 16504364862574, 174487098269718, 1915633726173390] "" "Class ", 3321, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3322, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [ [2, 3, 4, 1], {1, 2, 3}, {[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]}], [[1, 3, 2, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {4}, {[0, 1, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {3, 4}, {[0, 1, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 412, 2010, 10464, 57757, 336481, 2062062, 13257629, 89224136, 627342393, 4600113085, 35121030315, 278764459014, 2296946935932, 19620552655036, 173520474502403] "" "Class ", 3323, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3324, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3325, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3326, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3327, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 491, 2793, 17519, 119649, 880825, 6935395, 58037555, 513514788, 4783190038, 46730802425, 477346641225, 5084093543682, 56323877746954, 647652310692881, 7714953775226617] "" "Class ", 3328, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2664, 16338, 108984, 783314, 6021564, 49209454, 425372892, 3872830646, 37003897848, 369881122938, 3857272548080, 41864995750522, 471890131367364, 5513343369631830] "" "Class ", 3329, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3330, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3331, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2577, 15622, 103051, 732936, 5578977, 45171990, 387079192, 3495237142, 33135900270, 328761338650, 3404176630265, 36696637813076, 410938144076555, 4771075755829682] "" "Class ", 3332, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 3333, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3334, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3335, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2707, 16725, 112280, 811264, 6262312, 51336341, 444726973, 4054573303, 38765822514, 387509728073, 4039159877321, 43798171031016, 493028602042206, 5750807969031498] "" "Class ", 3336, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2321, 13304, 82517, 550000, 3917026, 29662646, 237838239, 2011610430, 17887297644, 166718080190, 1624375571901, 16504364862574, 174487098269718, 1915633726173390] "" "Class ", 3337, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3338, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1975, 10062, 53866, 301850, 1766812, 10791352, 68757051, 457034044, 3169950806, 22943915194, 173268853209, 1364549837364, 11196842312386, 95613949462398] "" "Class ", 3339, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3340, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3341, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3342, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3343, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3344, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3345, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3346, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3347, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2568, 15433, 100363, 700053, 5201196, 40930485, 339586999, 2958951221, 26988665050, 256951701275, 2547265363067, 26236347245903, 280219442661749, 3098173868016989] "" "Class ", 3348, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2281, 12770, 76385, 484288, 3234512, 22646762, 165566468, 1259723081, 9947281578, 81325205608, 686975613240, 5985068372367, 53692861290554, 495299052867755] "" "Class ", 3349, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3350, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3351, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3352, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3353, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3354, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3355, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2540, 15126, 97262, 669159, 4890540, 37751947, 306362728, 2603458041, 23091113192, 213148974500, 2042641702140, 20278194783305, 208142332182874, 2205167767929616] "" "Class ", 3356, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2237, 12297, 71879, 443390, 2869725, 19396979, 136401144, 994736593, 7503009058, 58397325491, 468065750737, 3856641906943, 32615299210241, 282707427418088] "" "Class ", 3357, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3358, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 1, 4, 2, 5], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[4, 1, 5, 2, 3], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 393, 1793, 8452, 40879, 201914, 1015113, 5182205, 26818012, 140515055, 744789784, 3991273391, 21617454493, 118314884656, 654344699623, 3657212613766] "" "Class ", 3359, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3360, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3361, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3362, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3363, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2653, 16159, 106736, 757766, 5741449, 46162458, 391998499, 3501698091, 32793890123, 321030201942, 3276539489781, 34786393927590, 383392588180369, 4378493409122485] "" "Class ", 3364, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2267, 12638, 75338, 476837, 3186803, 22390233, 164783735, 1266520249, 10139954259, 84376412929, 728320252996, 6510162492943, 60167298236572, 574149989667642] "" "Class ", 3365, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3366, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3367, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3368, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3369, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3370, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3371, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2825, 17811, 122176, 902786, 7130308, 59820538, 530385853, 4948564622, 48410437206, 495014997007, 5276436624591, 58488809771113, 672820525209345, 8016840243116836] "" "Class ", 3372, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2464, 14620, 94222, 653898, 4852660, 38286782, 319600060, 2810977706, 25956920588, 250869421958, 2530806542712, 26585245646806, 290175378811160, 3284599297937438] "" "Class ", 3373, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3374, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2184, 12096, 72104, 459440, 3111616, 22292592, 168263312, 1333377904, 11059335280, 95753379216, 863373139824, 8089902823120, 78625465178608, 791248858589264] "" "Class ", 3375, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3376, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3377, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3378, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3379, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2742, 17127, 116399, 852251, 6670557, 55467941, 487534557, 4510356515, 43761630805, 443920775044, 4695400132153, 51660893726108, 590006654493170, 6981335107629933] "" "Class ", 3380, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 441, 2308, 13180, 81362, 538890, 3806024, 28516766, 225688124, 1879727909, 16423797706, 150117819396, 1431853861689, 14220530001389, 146765050992614, 1571230819050993] "" "Class ", 3381, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3382, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3383, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 3, 2, 5], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 3, 2, 4], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 4, 2, 3], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2451, 14497, 93204, 646026, 4794894, 37890263, 317221324, 2801818750, 26010987743, 252992833957, 2570731154031, 27221092950467, 299693800379290, 3423717330177799] "" "Class ", 3384, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 1992, 10252, 55647, 317050, 1889423, 11744634, 75974552, 510466554, 3556197561, 25647327267, 191208294240, 1471610391911, 11677502387750, 95424615084196] "" "Class ", 3385, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {}], [[4, 2, 3, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {}], [[4, 2, 5, 3, 1], {1, 2, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 413, 2029, 10695, 60097, 358239, 2256511, 14969625, 104288083, 760984290, 5802270437, 46126129230, 381540685201, 3277662622617, 29192016835482, 269119568073139] "" "Class ", 3386, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 1, 5, 3, 4], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 1, 5, 2, 4], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 379, 1663, 7441, 33760, 154783, 715517, 3329756, 15581307, 73251934, 345753725, 1637632102, 7780027866, 37060264776, 176958541478, 846766263079] "" "Class ", 3387, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2595, 15723, 103340, 730016, 5502290, 43992963, 371347185, 3296019612, 30656961525, 297934364794, 3017512467329, 31778366585959, 347291836557132, 3931477903953444] "" "Class ", 3388, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2464, 14519, 92581, 633316, 4616868, 35681823, 291065036, 2496572164, 22445119033, 210916736748, 2066532403444, 21065275351747, 222964760818693, 2446147276150943] "" "Class ", 3389, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3390, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 0, 1]]} "Class ", 3391, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2127, 11382, 64520, 384772, 2401346, 15618563, 105512083, 738302103, 5338594346, 39812638817, 305685535675, 2412915479720, 19554782726800, 162517911410784] "" "Class ", 3392, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1973, 10016, 53202, 294028, 1684000, 9965836, 60805459, 381846654, 2464753738, 16335550758, 111069060325, 774172336446, 5528398119602, 40424331745892] "" "Class ", 3393, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 4, 2, 5], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}], [[4, 1, 5, 2, 3], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1974, 10034, 53400, 295740, 1696605, 10045920, 61218579, 383031676, 2455773390, 16107187742, 107921439662, 737756818396, 5140006025756, 36462029130960] "" "Class ", 3394, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}, {[[3, 1, 2, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 1, 5, 3, 4], {1, 2, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 5, 4, 2], {1, 2, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 3395, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]} {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]} "Class ", 3396, " is:" {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, {[[2, 4, 3, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 1, 4, 2, 5], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 364, 1525, 6425, 27155, 115023, 488045, 2073605, 8819990, 37548701, 159968443, 681913382, 2908267719, 12408343798, 52958862068, 226092174789] "" "Class ", 3397, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3398, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3399, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3400, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3401, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3402, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3403, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3404, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3405, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3406, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3407, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3408, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3409, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3410, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3411, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3412, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3413, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3414, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3415, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3416, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3417, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3418, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3419, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 1, 1]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 415, 2065, 11118, 64273, 396282, 2591308, 17888061, 129853123, 987969890, 7855640015, 65112088857, 561312858276, 5022709493594, 46566776902041, 446591463537803] "" "Class ", 3420, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3421, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3422, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3423, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3424, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3425, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3426, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3427, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3428, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3429, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3430, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3431, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3432, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3433, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3434, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3435, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3436, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3437, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3438, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3439, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3440, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3441, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3442, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3443, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3444, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3445, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3446, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3447, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3448, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3449, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3450, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3451, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3452, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3453, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}}, " the pattern set ", {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[1, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2150, 11708, 68282, 423948, 2788230, 19341952, 141003552, 1076787624, 8589843716, 71404154928, 617151121998, 5535236798058, 51426766394244, 494145546973656] "" "Class ", 3454, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3455, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3456, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3457, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3458, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3459, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3460, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3461, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3462, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3463, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3464, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3465, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3466, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3467, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3468, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3469, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3470, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3471, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3472, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3473, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3474, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3475, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3476, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3477, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3478, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3479, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3480, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3481, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3482, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3483, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3484, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3485, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3486, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]} "Class ", 3487, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3488, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3489, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3490, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3491, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3492, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3493, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3494, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, {[[3, 1, 2, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [0, 1, 1]]} "Class ", 3495, " is:" {{[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]} {[[2, 4, 3, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3496, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3497, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3498, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3499, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3500, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3501, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3502, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3503, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3504, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3505, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3506, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3507, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3508, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3509, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3510, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3511, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3512, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3513, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3514, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 2, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 4, 1, 3, 5], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2}, {}], [[3, 4, 1, 2, 5], {1, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 2, 4], {3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {}], [[3, 5, 2, 4, 1], {1, 2}, {}], [[4, 5, 1, 2, 3], {3}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 1, 3, 2], {1, 2}, {}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 382, 1707, 7855, 36964, 177045, 860210, 4229293, 21001875, 105181880, 530655569, 2694429442, 13758466106, 70606691167, 363967280138, 1883748263033] "" "Class ", 3515, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3516, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3517, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3518, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3519, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3520, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3521, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3522, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3523, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3524, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3525, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3526, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3527, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3528, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3529, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3530, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3531, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3532, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3533, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3534, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3535, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3536, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3537, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3538, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3539, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3540, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 2, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 2, 0]}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 366, 1552, 6652, 28696, 124310, 540040, 2350820, 10248248, 44725516, 195354368, 853829272, 3733693872, 16333556838, 71476391800, 312865382004] "" "Class ", 3541, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 3542, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3543, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3544, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3545, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3546, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3547, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3548, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3549, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3550, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3551, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3552, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3553, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3554, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3555, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3556, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3557, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3558, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3559, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3560, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3561, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3562, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3563, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3564, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3565, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3566, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3567, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3568, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3569, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3570, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3571, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3572, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3573, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3574, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3575, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3576, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 3577, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3578, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3579, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3580, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3581, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3582, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3583, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} "Class ", 3584, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {[0, 1, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 1, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {4}, {[0, 0, 1, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 1, 1, 0], [0, 1, 0, 1, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 1, 1, 0], [0, 1, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {[0, 1, 0, 1, 0], [0, 1, 1, 0, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {}, {[0, 1, 0, 1, 0], [0, 1, 1, 0, 0]}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 1, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {4}, {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3}, %2], [[2, 1, 5, 3, 4], {1, 5}, {[0, 0, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, %2], [[2, 5, 1, 3, 4], {3, 5}, {[0, 0, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 5, 1, 4, 3], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0]}], [[3, 1, 4, 2, 5], {1, 2, 3}, %2], [[3, 1, 5, 2, 4], {1, 5}, {[0, 0, 0, 1, 1, 0], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 5, 1, 2, 4], {3}, {[0, 0, 0, 1, 1, 0], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 5, 1, 4, 2], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2, 3}, %1], [[4, 1, 5, 2, 3], {1, 5}, {[0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [4, 1, 5, 3, 2], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3}, %1], [[4, 5, 1, 2, 3], {3}, {[0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [4, 5, 1, 3, 2], {1, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2, 3}, %1]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %2 := {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 338, 1318, 5106, 19718, 76066, 293398, 1131794, 4366374, 16846018, 64995254, 250765298, 967503814, 3732821922, 14401956182, 55565542354] "" "Class ", 3585, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3416, 24582, 198930, 1788762, 17692576, 190906106, 2231584732, 28092650826, 378909707266, 5451392818206, 83331307383260, 1348753235970776, 23042940248582440, 414399935662053250] "" "Class ", 3586, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 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}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3045, 20531, 154421, 1282265, 11653069, 115047810, 1226152279, 14030525843, 171559587620, 2232397480211, 30800565508686, 449125370213049, 6901403294433136, 111463633207258601] "" "Class ", 3587, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 3588, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 3589, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[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, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3064, 20672, 155189, 1283024, 11582523, 113361634, 1195618841, 13518225402, 163109478438, 2091918680618, 28417723573488, 407616831535417, 6156210446886014, 97650275725613315] "" "Class ", 3590, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 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, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 478, 2653, 16159, 106736, 757766, 5741449, 46162458, 391998499, 3501698091, 32793890123, 321030201942, 3276539489781, 34786393927590, 383392588180369, 4378493409122485] "" "Class ", 3591, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 3592, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 3593, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 554, 3538, 25822, 212000, 1934114, 19409369, 212487482, 2520102562, 32187510690, 440473505213, 6429553637752, 99717371553283, 1637511622825772, 28384356793932980, 517905018431305466] "" "Class ", 3594, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 519, 3108, 20922, 156381, 1284843, 11509557, 111642508, 1165768984, 13037988395, 155492501710, 1969811855946, 26415797127349, 373847535077080, 5568283833289840, 87069234923254713] "" "Class ", 3595, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 2, 5], {2, 3}, {}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3}, {}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3056, 20509, 152755, 1249533, 11130554, 107212809, 1110070281, 12291732347, 144916143382, 1812106192169, 23951525475057, 333617730162140, 4883749709578630, 74952353482652167] "" "Class ", 3596, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 490, 2762, 17120, 115283, 835644, 6474223, 53302184, 464078016, 4255519635, 40955353256, 412425999997, 4334132512261, 47419447616971, 539010874703418, 6353418723588266] "" "Class ", 3597, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3069, 20778, 156862, 1306740, 11908106, 117840304, 1258429893, 14424891210, 176650423998, 2301739488241, 31795443695579, 464132352374148, 7138945844521249, 115401924551064028] "" "Class ", 3598, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3599, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {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}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2684, 16529, 110787, 800767, 6196137, 51019578, 444823409, 4089205803, 39492690392, 399442489207, 4219426779140, 46436017799791, 531269829891690, 6306491950543603] "" "Class ", 3600, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3601, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 506, 3038, 20580, 155244, 1290582, 11719920, 115399416, 1224388964, 13924299771, 168955879460, 2178583020714, 29746560729295, 428740302578724, 6504650354520289, 103615563662925712] "" "Class ", 3602, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3603, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3604, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 506, 3034, 20499, 154129, 1276225, 11533362, 112928392, 1190780745, 13451382546, 162044969549, 2073564940858, 28086391097010, 401439880007207, 6037863859543939, 95322798557838146] "" "Class ", 3605, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2438, 14209, 89005, 594130, 4198503, 31245559, 243863200, 1989172878, 16908636756, 149409675237, 1369464366086, 12995918829570, 127474330691309, 1290475587618730] "" "Class ", 3606, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3607, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3608, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 545, 3473, 25318, 207584, 1890955, 18947051, 207107414, 2452540173, 31276705724, 427355191556, 6228528209384, 96451910955831, 1581465987911605, 27370956373343878, 498650759667793107] "" "Class ", 3609, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3105, 21243, 162231, 1367633, 12610570, 126222154, 1362730246, 15783239716, 195189382979, 2566907713755, 35767662799329, 526387212831500, 8158500310181774, 132827043702874108] "" "Class ", 3610, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3611, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3612, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3041, 20418, 152487, 1253623, 11250890, 109448479, 1147162270, 12887842938, 154496043961, 1968413027246, 26561631574366, 378422015801204, 5676291327414354, 89417497324033793] "" "Class ", 3613, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 479, 2668, 16334, 108590, 776846, 5937492, 48200625, 413600025, 3736037799, 35401749834, 350835409895, 3626545529825, 39009792286722, 435748642897613, 5045045772327322] "" "Class ", 3614, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3615, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3616, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 548, 3498, 25512, 209276, 1907444, 19125416, 209195760, 2478873088, 31633000800, 432503767944, 6307662171408, 97740780804312, 1603639416084240, 27772741230939560, 506299118952551808] "" "Class ", 3617, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 504, 3004, 20185, 150970, 1243713, 11188826, 109132256, 1147011526, 12922707061, 155358576197, 1985092837160, 26863328916577, 383804536005238, 5773129284559066, 91193458573840207] "" "Class ", 3618, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 3619, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 3620, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {[0, 0, 1, 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}, {[0, 0, 0, 1, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3141, 21594, 165644, 1402007, 12977010, 130377700, 1412854291, 16425369055, 203905499530, 2691946601026, 37658644991630, 556461019372158, 8660321639224629, 141593772577761816] "" "Class ", 3621, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 3622, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 3623, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 3624, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 567, 3680, 27282, 227539, 2108657, 21495664, 239046831, 2879894437, 37364145855, 519393872879, 7701357801884, 121329583504513, 2023903011503090, 35636396624583853, 660502196089052682] "" "Class ", 3625, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 521, 3140, 21316, 160913, 1336465, 12108262, 118815491, 1255190241, 14201761261, 171326037613, 2195066406458, 29765186772714, 425859062135963, 6410900900858142, 101294639972203874] "" "Class ", 3626, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 3627, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 3628, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 527, 3238, 22542, 175213, 1503132, 14101640, 143574229, 1576321275, 18561469018, 233314254966, 3117843211837, 44135413264812, 659709002202589, 10382696720587089, 171611320152584821] "" "Class ", 3629, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 3630, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 3631, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 3632, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 547, 3485, 25392, 208054, 1894161, 18970063, 207252952, 2453001528, 31266366163, 426992870628, 6220033785862, 96270604186902, 1577677676373018, 27291281566058975, 496942320343791033] "" "Class ", 3633, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3103, 21121, 160077, 1336841, 12194163, 120603551, 1285387339, 14684942021, 179013962969, 2319191204798, 31818873684512, 460856333207763, 7026773709981822, 112500637384646123] "" "Class ", 3634, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3635, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3636, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2972, 19814, 146923, 1199181, 10682199, 103122707, 1072380226, 11950604975, 142076077619, 1794839540580, 24009629009331, 339037808949177, 5039664196391083, 78659840490936564] "" "Class ", 3637, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2595, 15723, 103340, 730016, 5502290, 43992963, 371347185, 3296019612, 30656961525, 297934364794, 3017512467329, 31778366585959, 347291836557132, 3931477903953444] "" "Class ", 3638, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3639, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 0]]} "Class ", 3640, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2939, 19522, 144297, 1174521, 10438158, 100559491, 1043781687, 11612222621, 137838489770, 1738794080694, 23228581675512, 327594247653079, 4863760069834211, 75828730083693932] "" "Class ", 3641, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3642, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3643, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2972, 19928, 148868, 1225279, 11015543, 107390139, 1128317805, 12708996868, 152762005287, 1951661455714, 26408464675683, 377281183379921, 5674755353792694, 89636999730137205] "" "Class ", 3644, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 1, 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, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 2, 4, 5], {2, 3, 4}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 450, 2360, 13411, 81821, 531927, 3663079, 26591437, 202674001, 1616429400, 13451651059, 116514870939, 1048176872117, 9774698782039, 94328795886346, 940562197200666] "" "Class ", 3645, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3646, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3647, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 546, 3479, 25345, 207727, 1891636, 18948363, 207058711, 2451192290, 31249712275, 426852583466, 6219257463641, 96278229880844, 1578124423275505, 27304578758188359, 497285865407686604] "" "Class ", 3648, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 503, 2990, 20038, 149457, 1227738, 11013070, 107103838, 1122406161, 12608798270, 151148746652, 1925813521559, 25988125014974, 370276630140669, 5554553318138024, 87507349539707768] "" "Class ", 3649, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3650, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {2, 3}, {[0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2604, 15908, 105921, 761732, 5873647, 48269622, 420618263, 3869569532, 37442825596, 379828316616, 4027845938832, 44537164681509, 512335146485108, 6119092703106332] "" "Class ", 3651, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3099, 21127, 160632, 1347427, 12360205, 123080041, 1322152402, 15239889027, 187616164292, 2456852217591, 34099381388028, 500015045007095, 7724035401363574, 125374441065946103] "" "Class ", 3652, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3653, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2700, 16715, 112730, 820386, 6393921, 53041241, 465948054, 4315854470, 41995279630, 427910570908, 4553163432302, 50467638788972, 581437254405195, 6949173993793475] "" "Class ", 3654, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]} "Class ", 3655, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 554, 3539, 25845, 212314, 1937981, 19458994, 213147093, 2529305516, 32322716641, 442565538408, 6463623590406, 100300581711958, 1647989456660991, 28581597693758610, 521789060371317603] "" "Class ", 3656, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3083, 20941, 158679, 1326984, 12139886, 120601315, 1292840550, 14874702423, 182821573749, 2390567664722, 33135733071840, 485305978997884, 7488699817167367, 121434424402923873] "" "Class ", 3657, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 3658, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 3659, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 3, 2, 5], {1, 2, 3}, {}], [[5, 1, 3, 2, 4], {2, 3}, {}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {2, 3, 4}, {}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3174, 21766, 166304, 1400925, 12896390, 128791661, 1386719755, 16012687261, 197386208646, 2586997337795, 35921635907892, 526771118949671, 8135080171721721, 131967265146003064] "" "Class ", 3660, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 3}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2678, 16416, 109216, 781229, 5964805, 48327761, 413508209, 3721378369, 35104337515, 346070131926, 3556203602949, 38004430622817, 421524560509062, 4843513456257911] "" "Class ", 3661, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 3662, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 3663, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 522, 3168, 21750, 166628, 1408852, 13028138, 130781555, 1416170335, 16452877245, 204123906490, 2693365193702, 37659934327998, 556230777707667, 8653197108818988, 141424250544673833] "" "Class ", 3664, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3665, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3666, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 523, 3179, 21847, 167434, 1415496, 13083569, 131244466, 1419900504, 16479015176, 204213854968, 2691260270704, 37582501743822, 554358220136418, 8612526962251157, 140569090359893761] "" "Class ", 3667, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {1, 3}, {}], [[2, 4, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 474, 2586, 15341, 97854, 665444, 4792793, 36369748, 289552850, 2410079670, 20910817419, 188647637089, 1765721548100, 17113916400187, 171472037232198, 1773341405260174] "" "Class ", 3668, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 3669, " is:" {{[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 3670, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3671, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3672, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3673, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 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}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3100, 21143, 160899, 1351326, 12413680, 123806199, 1332147059, 15381153274, 189681166334, 2488186404306, 34593792027366, 508132214201288, 7862696145885716, 127837895873280100] "" "Class ", 3674, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2810, 18322, 133234, 1070126, 9414260, 90057994, 930958238, 10343283702, 122928834458, 1556358375506, 20913412144340, 297283978326242, 4457262013467746, 70300645460855990] "" "Class ", 3675, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 3676, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 3677, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[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, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2790, 17903, 126965, 986075, 8324872, 75920825, 743925957, 7795836897, 87013131016, 1030679879049, 12914460498958, 170679369108291, 2373004095748690, 34625315153576903] "" "Class ", 3678, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2443, 14352, 91333, 624640, 4561956, 35391648, 290357898, 2509418819, 22769704890, 216271249710, 2144639780723, 22151496424455, 237808684815655, 2648501674187504] "" "Class ", 3679, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 3680, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 3681, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3138, 21543, 165055, 1395507, 12903242, 129507220, 1402100263, 16285882578, 202005265959, 2664768110029, 37250905045682, 550052768615868, 8554957831215658, 139784047638836056] "" "Class ", 3682, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 485, 2774, 17730, 125223, 968451, 8141034, 73914061, 720854172, 7515973942, 83432333742, 982424179188, 12230941083548, 160526024363241, 2215189154117757, 32064142850556796] "" "Class ", 3683, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 476, 2700, 17066, 118953, 905991, 7483971, 66641724, 636341344, 6486326349, 70300810079, 807352643648, 9794050385771, 125155925636453, 1680512390509847, 23656187441110008] "" "Class ", 3684, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [ [2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2455, 14470, 92455, 635187, 4662222, 36367129, 300118626, 2610174906, 23844354945, 228119927759, 2279666154844, 23741089197570, 257125531428614, 2890590345928365] "" "Class ", 3685, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3686, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3687, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3688, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3689, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2532, 15420, 102620, 739512, 5729192, 47429896, 417429800, 3888426512, 38192416048, 394239339792, 4264424937488, 48212317486112, 568395755184224, 6973300915138656] "" "Class ", 3690, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3691, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3692, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3693, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3694, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3695, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2939, 19496, 143650, 1163194, 10261879, 97943219, 1005353037, 11041923056, 129191539936, 1604005931154, 21060968111343, 291563666572811, 4244154964400143, 64802078628450244] "" "Class ", 3696, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 469, 2598, 15923, 106784, 776662, 6081880, 50967416, 454750348, 4301056798, 42958549822, 451598655332, 4982069092072, 57529048070188, 693696896374292, 8716516562283788] "" "Class ", 3697, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3698, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3699, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3700, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3701, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3702, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3703, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 504, 3005, 20173, 150487, 1234874, 11052189, 107116418, 1117432139, 12482636336, 148652044775, 1879805575456, 25155292808675, 355126877963267, 5274464611330595, 82212011057622554] "" "Class ", 3704, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 460, 2532, 15420, 102620, 739512, 5729192, 47429896, 417429800, 3888426512, 38192416048, 394239339792, 4264424937488, 48212317486112, 568395755184224, 6973300915138656] "" "Class ", 3705, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 3706, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 3707, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 3708, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 3709, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 3710, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 3711, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 538, 3336, 23389, 182820, 1575699, 14840680, 151610438, 1669452844, 19708898042, 248303595779, 3324912602598, 47152714611584, 705973195588973, 11127456467022160, 184172227337008905] "" "Class ", 3712, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 97, 497, 2897, 18913, 136636, 1081817, 9312400, 86576130, 864385805, 9223064292, 104727773185, 1260818639675, 16040480403252, 215020864419797, 3028986865647987, 44733623524130485] "" "Class ", 3713, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 3714, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 3715, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 3716, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 3717, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 3718, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 3719, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 506, 3044, 20693, 156821, 1310548, 11969893, 118600165, 1266846301, 14510663659, 177405653357, 2305730778292, 31744041197674, 461479253684673, 7063942859790090, 113563508436981919] "" "Class ", 3720, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 476, 2718, 17388, 123208, 957953, 8108663, 74230591, 730782116, 7699085861, 86433090443, 1030085774947, 12988687922188, 172764959382377, 2417547923078647, 35503082711965650] "" "Class ", 3721, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3722, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3723, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3724, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3725, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3726, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 0]]} "Class ", 3727, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[1, 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, 6, 22, 94, 463, 2590, 16246, 112996, 863140, 7183001, 64683173, 626635818, 6498255773, 71818347252, 842674214616, 10461376145330, 136994143320099, 1887183044415917, 27280689740404740] "" "Class ", 3728, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3729, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3730, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3731, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3732, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3733, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2948, 19559, 144138, 1167570, 10307818, 98485708, 1012330933, 11137864782, 130584305943, 1625199305308, 21397441183986, 297120789375784, 4339446187994541, 66496193623036085] "" "Class ", 3734, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2483, 14868, 97056, 684761, 5185095, 41893424, 359392528, 3259834475, 31148672459, 312545979000, 3283938029756, 36040837059503, 412230564514829, 4904045619272402] "" "Class ", 3735, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[2, 5, 4, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[3, 4, 1, 5, 2], {1, 3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 457, 2477, 14750, 95483, 666405, 4980752, 39642749, 334429331, 2978374887, 27905365128, 274231262774, 2819089047407, 30243559425311, 337883168528996, 3923541236037066] "" "Class ", 3736, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 4, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2144, 11576, 66424, 402246, 2556919, 16987488, 117542228, 844557382, 6285605863, 48351824157, 383719085244, 3136424958232, 26366044853793, 227656007260611] "" "Class ", 3737, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3738, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3739, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3740, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3741, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 508, 3008, 20020, 147871, 1199957, 10608505, 101468038, 1043840896, 11491388151, 134784134561, 1677882372779, 22093435892278, 306780839702609, 4479988118671081, 68635002377801358] "" "Class ", 3742, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2586, 15838, 106501, 780384, 6190409, 52859325, 483437237, 4714750242, 48840717960, 535557043366, 6197089975997, 75461388664863, 964565236722590, 12912933081184587] "" "Class ", 3743, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 3744, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 3745, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2727, 17112, 117686, 878743, 7069670, 60897479, 558677620, 5434047075, 55820372797, 603521812690, 6847387966104, 81308550135593, 1008085582089514, 13022165229557375] "" "Class ", 3746, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2283, 12807, 76855, 489439, 3287228, 23169592, 170691442, 1309936666, 10442360060, 86257603939, 736762493537, 6495069727667, 59000325170402, 551448280788469] "" "Class ", 3747, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 3748, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 3749, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3750, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3751, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2803, 18163, 130777, 1036932, 8985831, 84554732, 859088719, 9377799500, 109499631018, 1362273172808, 17993740869264, 251536396774858, 3710643811991217, 57613942390283874] "" "Class ", 3752, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2234, 12260, 71546, 440773, 2850311, 19258636, 135456888, 988766202, 7471310266, 58313780250, 469252610622, 3886829009489, 33091210716707, 289202744547213] "" "Class ", 3753, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]} "Class ", 3754, " is:" {{[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 3755, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3756, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 2, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 3757, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 3758, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 3759, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 3760, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 3761, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 3762, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 3763, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 3764, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 3765, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3766, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3767, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3768, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3769, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3770, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3771, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3772, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3773, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3774, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3775, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3776, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3777, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3778, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3779, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3780, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3781, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3782, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3783, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3784, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3785, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3786, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 3787, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 3788, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 3789, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 3790, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 3791, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 3792, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 3793, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 3794, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 3795, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 3796, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 3797, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 3798, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 3799, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 3800, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 3801, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 3802, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3803, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3804, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3805, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3806, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3807, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3808, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3809, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 0]]} "Class ", 3810, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3811, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3812, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3813, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3814, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3815, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3816, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3817, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3818, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3819, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3820, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3821, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3822, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3823, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 3824, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 3825, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 3826, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 3827, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 3828, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 3829, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 3830, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 3831, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3832, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]} "Class ", 3833, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 3834, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 3835, " is:" {{[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 3836, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3837, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3838, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3839, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 3840, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 3841, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 3842, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 2, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 420, 2042, 10404, 54954, 298648, 1660714, 9410772, 54174212, 316038060, 1864781388, 11111804604, 66782160002, 404392312896, 2465100947836, 15116060536540] "" "Class ", 3843, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 3844, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 3845, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 3846, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 3847, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3848, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3849, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3850, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3851, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3852, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3853, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3854, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3855, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3856, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3857, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3858, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3859, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3860, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3861, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3862, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3863, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3864, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3865, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3866, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3867, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 3868, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 3869, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 3870, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 3871, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 3872, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 3873, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 3874, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 3875, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 3876, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 3877, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 3878, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 3879, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 3880, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 3881, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 3882, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 3883, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3884, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3885, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3886, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3887, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3888, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3889, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3890, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 0]]} "Class ", 3891, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3892, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3893, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3894, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3895, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3896, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3897, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3898, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 395, 1823, 8741, 43192, 218677, 1129519, 5932605, 31603937, 170408865, 928500329, 5105360024, 28297178891, 157954119674, 887263190868, 5012123024566] "" "Class ", 3899, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3900, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3901, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3902, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3903, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 3904, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 3905, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 3906, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 3907, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 3908, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 3909, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 3910, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 3911, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3912, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3913, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]} "Class ", 3914, " is:" {{[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}} {[[1, 4, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 3915, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 509, 3021, 20153, 149135, 1212220, 10731983, 102775805, 1058432379, 11662976021, 136909331832, 1705566481413, 22472173309937, 312213249712089, 4561546585502297, 69914542716568008] "" "Class ", 3916, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 3917, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 3918, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 3919, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2730, 17172, 118520, 889116, 7194004, 62383568, 576677816, 5656891176, 58653066696, 640584346608, 7347121283680, 88255946135376, 1107672668696048, 14493714457542656] "" "Class ", 3920, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 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}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2411, 13963, 87042, 579259, 4088943, 30457287, 238374743, 1953283669, 16706473009, 148757363759, 1375787882351, 13189453993725, 130835235093995, 1340746108292891] "" "Class ", 3921, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 3922, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 3923, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3047, 20441, 152216, 1245485, 11103016, 107084298, 1110754080, 12328393419, 145773361218, 1829177305436, 24274986654747, 339680261402369, 4998153522518463, 77146010685673727] "" "Class ", 3924, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 480, 2693, 16694, 113045, 828745, 6530086, 54971124, 491886472, 4658263255, 46513472729, 488090203605, 5366942774266, 61679136438578, 739147080230889, 9217260060685415] "" "Class ", 3925, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}], [[3, 2, 4, 5, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 471, 2625, 16192, 109234, 798484, 6277296, 52745869, 471253102, 4457010567, 44452402917, 465973086577, 5118784438055, 58773865046680, 703728587993330, 8768480260481785] "" "Class ", 3926, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2403, 13801, 84813, 552872, 3797408, 27336915, 205377633, 1604614816, 12999524325, 108929166774, 942099454273, 8394307622973, 76932313049202, 724187774518828] "" "Class ", 3927, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2619, 16215, 110363, 818681, 6572211, 56757931, 524625343, 5167322810, 54025643671, 597547214738, 6970513055371, 85525669713835, 1101038620544936, 14839445026575945] "" "Class ", 3928, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 3929, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [ [2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}] , [[3, 2, 4, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 440, 2289, 12930, 78532, 508940, 3497940, 25370260, 193377082, 1543573391, 12864158436, 111642368305, 1006634813961, 9410810018836, 91055698175189, 910345106104045] "" "Class ", 3930, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 3931, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 3932, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 1996, 10321, 56385, 323449, 1938892, 12099377, 78363969, 525449613, 3639959011, 26003549267, 191276358093, 1446724557361, 11237666279830, 89548180694231] "" "Class ", 3933, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 3934, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3}, {}], [[1, 2, 4, 5, 3], {2, 3}, {}], [[1, 3, 2, 4, 5], {2}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 502, 2993, 20211, 152350, 1267467, 11531372, 113873006, 1212852743, 13857812922, 169062059678, 2193234151438, 30147028103851, 437656542940420, 6691258268444141, 107460436249648746] "" "Class ", 3935, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2}, {[1, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {}], [[1, 3, 4, 2], {2}, {[1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2667, 16823, 117484, 900394, 7516849, 67918544, 660481162, 6879045277, 76404745856, 901529339887, 11262379448400, 148507385397767, 2061303660065329, 30042329755819835] "" "Class ", 3936, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3937, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3938, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[1, 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, 6, 22, 95, 473, 2676, 16953, 118952, 915522, 7668776, 69447616, 676075297, 7040585151, 78097930239, 919285631089, 11444318431012, 150231664127581, 2073959239622604, 30036808822644479] "" "Class ", 3939, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[1, 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, 6, 22, 93, 442, 2320, 13277, 82081, 544169, 3845869, 28833645, 228373611, 1904055475, 16658863469, 152527057177, 1457868185203, 14514521444759, 150222782619019, 1613362659261770] "" "Class ", 3940, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3941, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3942, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 517, 3139, 21559, 165189, 1396529, 12911721, 129582710, 1402825791, 16293471307, 202091592412, 2665838117565, 37265362671125, 550265171258658, 8558333937608963, 139841713515791890] "" "Class ", 3943, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2679, 16913, 118016, 902154, 7499730, 67380858, 650739960, 6723674428, 74016201636, 864890769962, 10692370583574, 139436029905684, 1912932355586610, 27541762178083919] "" "Class ", 3944, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 3945, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 3946, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 490, 2864, 18878, 138644, 1123114, 9952036, 95787806, 995385116, 11109019658, 132546426364, 1683861088478, 22694736522076, 323463498694682, 4861257732679452, 76834916185539086] "" "Class ", 3947, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 3948, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 3949, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 3950, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 522, 3154, 21440, 161919, 1344435, 12168512, 119205696, 1256373334, 14173494152, 170388885743, 2174312275892, 29351314233978, 417860925299024, 6256719277288803, 98288366688512899] "" "Class ", 3951, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2724, 17058, 116986, 870550, 6975982, 59816932, 545936024, 5279481434, 53885926694, 578513658428, 6513334428452, 76698980950720, 942412660997464, 12056789857666612] "" "Class ", 3952, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 3953, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 3954, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 483, 2748, 17406, 121323, 922079, 7584897, 67112204, 635396785, 6407976739, 68568548838, 775817823886, 9253334199209, 116026026525164, 1525689291383053, 20992649981851907] "" "Class ", 3955, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 3956, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 3957, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 3958, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {2, 3, 4}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2961, 19695, 145392, 1178992, 10414176, 99504794, 1022363219, 11238243476, 131586940514, 1634841616802, 21478826262169, 297511692083555, 4332907770980374, 66187588853680266] "" "Class ", 3959, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2614, 16119, 108963, 800269, 6338455, 53806457, 486980117, 4677966529, 47508763750, 508360843046, 5713954104819, 67281725629669, 827951845963051, 10624702355583537] "" "Class ", 3960, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 3961, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 3962, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2468, 14710, 95562, 670988, 5056920, 40670280, 347338320, 3136772116, 29845742664, 298238193182, 3121048946778, 34119674096412, 388777200157152, 4607973479432672] "" "Class ", 3963, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2127, 11382, 64520, 384772, 2401346, 15618563, 105512083, 738302103, 5338594346, 39812638817, 305685535675, 2412915479720, 19554782726800, 162517911410784] "" "Class ", 3964, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 3965, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[3, 2, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 0, 1]]} "Class ", 3966, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3967, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 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}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 412, 2007, 10420, 57374, 334005, 2050634, 13246282, 89816367, 637763738, 4731681535, 36599692672, 294552636839, 2461826153262, 21331126162975, 191314729500825] "" "Class ", 3968, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3969, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3121, 21424, 164187, 1388855, 12849399, 129046707, 1397982669, 16247987176, 201654743175, 2661658773874, 37227644289987, 549992767926380, 8558202735812834, 139901669721238885] "" "Class ", 3970, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 473, 2668, 16831, 117474, 898899, 7483475, 67343889, 651440126, 6741180269, 74309915119, 869333709516, 10757577880307, 140391622610693, 1927107112831560, 27756085813786258] "" "Class ", 3971, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3972, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3973, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 487, 2823, 18455, 134510, 1082392, 9536242, 91331303, 944998941, 10507179879, 124953732786, 1582803928826, 21277883184519, 302574456833555, 4537983650379768, 71592767060398068] "" "Class ", 3974, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3975, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2463, 14612, 94227, 654992, 4874597, 38621288, 324205702, 2871691606, 26744402713, 261067798256, 2663821233105, 28341747455790, 313738532399833, 3606396930456404] "" "Class ", 3976, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]} "Class ", 3977, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3104, 21202, 161572, 1358658, 12494534, 124730288, 1343207518, 15520322620, 191523723392, 2513844304920, 34969174891314, 513894241860266, 7955349119465418, 129396171343586284] "" "Class ", 3978, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 474, 2693, 17214, 122540, 962743, 8282974, 77510004, 784234851, 8534601539, 99440091109, 1235361621268, 16303584617030, 227820671377207, 3360697133968851, 52193830924393828] "" "Class ", 3979, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 3980, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 3981, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {3, 4}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {1, 3, 4}, {}], [[4, 1, 3, 2, 5], {1, 3, 4}, {}], [[5, 1, 3, 2, 4], {3, 4}, {}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2768, 17712, 125400, 973488, 8223880, 75116680, 737741056, 7753302432, 86825816384, 1032208763680, 12983680635040, 172284211349632, 2405164117757920, 35240342998767968] "" "Class ", 3982, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {1, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2321, 13304, 82517, 550000, 3917026, 29662646, 237838239, 2011610430, 17887297644, 166718080190, 1624375571901, 16504364862574, 174487098269718, 1915633726173390] "" "Class ", 3983, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 3984, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 3985, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {3}, {}], [[2, 5, 4, 3, 1], {1, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2252, 12476, 73804, 463166, 3068157, 21368873, 155967531, 1189702015, 9461417673, 78283857509, 672613458780, 5990912033383, 55230082825467, 526247864888194] "" "Class ", 3986, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 3987, " is:" {{[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 3988, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 3989, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 4, 1], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3, 5], {2, 3}, {[0, 0, 0, 1, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 4, 2], {3, 5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 476, 2613, 15621, 100499, 689760, 5016508, 38456156, 309400201, 2603252463, 22837386312, 208349367672, 1972346077437, 19336046232871, 195970811974815, 2050123807248940] "" "Class ", 3990, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 451, 2380, 13612, 83500, 545089, 3763809, 27356625, 208474555, 1660222424, 13778031716, 118869434846, 1063907752240, 9860189881458, 94471176795754, 934339408526914] "" "Class ", 3991, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 3992, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 3993, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 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}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 453, 2411, 13963, 87042, 579259, 4088943, 30457287, 238374743, 1953283669, 16706473009, 148757363759, 1375787882351, 13189453993725, 130835235093995, 1340746108292891] "" "Class ", 3994, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2146, 11624, 67146, 411142, 2656052, 18035178, 128318314, 954086192, 7396278762, 59659032142, 499778527628, 4341025729290, 39035256389026, 362878164902216] "" "Class ", 3995, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 3996, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 3997, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 1, 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, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2546, 15126, 96744, 660227, 4775252, 36410538, 291421229, 2439692182, 21299342533, 193418572333, 1822892396445, 17795187484553, 179624952058623, 1871874822975630] "" "Class ", 3998, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 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}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2265, 12592, 74690, 469318, 3107135, 21582637, 156756077, 1187146005, 9352342378, 76488324556, 648279878963, 5685189470199, 51515187694859, 481708095353713] "" "Class ", 3999, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 1, 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, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 428, 2178, 11965, 70272, 438082, 2883051, 19942523, 144474663, 1092943126, 8611998939, 70529060180, 599191173961, 5271881532629, 47963952865019, 450632432825778] "" "Class ", 4000, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {4}, %1], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 1, 3, 4], {3}, %1], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, %1], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} %1 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 412, 2005, 10352, 56185, 318481, 1876614, 11454416, 72229768, 469575717, 3142220836, 21614753829, 152684752749, 1106630363373, 8223560449893, 62617983379215] "" "Class ", 4001, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4002, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4003, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4004, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4005, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4006, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4007, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 2, 4, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 4, 5], {2}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 449, 2345, 13192, 79087, 501340, 3339815, 23269744, 168902858, 1273102740, 9937935871, 80156408539, 666698535957, 5708493678288, 50240725252499, 453888177851968] "" "Class ", 4008, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[1, 3, 2, 4], {}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 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, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[1, 3, 2, 5, 4], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2094, 11021, 61123, 354956, 2147730, 13487539, 87628414, 587443831, 4054332186, 28751921031, 209161082113, 1558560232804, 11880381974383, 92533367860538] "" "Class ", 4009, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4010, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4011, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4012, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4013, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4014, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4015, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2509, 14688, 92236, 616052, 4348350, 32273780, 250870715, 2035566896, 17192651591, 150794367605, 1370611305538, 12886773313093, 125134987178265, 1253129730597150] "" "Class ", 4016, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2126, 11365, 64329, 382921, 2384397, 15466405, 104151803, 726107914, 5228595816, 38812054217, 296493536072, 2327535291681, 18752211312599, 154878029580823] "" "Class ", 4017, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4018, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4019, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2263, 12551, 74106, 462105, 3024455, 20675393, 147052508, 1084766241, 8277822722, 65202042246, 529121940839, 4416626537945, 37865429250646, 333012489281441] "" "Class ", 4020, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4021, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4022, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4023, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 489, 2737, 16689, 109481, 765798, 5673088, 44273703, 362431816, 3101111915, 27651557490, 256284014107, 2463544340390, 24512775112753, 252040970718725, 2673805987813294] "" "Class ", 4024, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 94, 453, 2405, 13842, 85422, 560781, 3892733, 28436749, 217761667, 1742435863, 14528439012, 125934927505, 1132522577212, 10547114009384, 101555694768836, 1009548032413085] "" "Class ", 4025, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4026, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4027, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4028, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4029, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4030, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4031, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2432, 14191, 89086, 596433, 4231802, 31660295, 248726935, 2044712898, 17537159703, 156530742184, 1450741552036, 13934118174259, 138455279290365, 1421016371303109] "" "Class ", 4032, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2144, 11685, 68270, 424746, 2799434, 19462000, 142209017, 1088802184, 8711241259, 72657262325, 630396122490, 5678612890457, 53015352411881, 512147683798197] "" "Class ", 4033, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4034, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4035, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4036, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4037, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4038, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[3, 2, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 0, 1]]} "Class ", 4039, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4040, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4041, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 462, 2465, 14205, 87481, 571227, 3930523, 28359149, 213691771, 1676049541, 13645081171, 115033023191, 1002155611383, 9006086974533, 83356391580544, 793472567001062] "" "Class ", 4042, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 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, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2096, 11055, 61542, 359355, 2190322, 13881175, 91176190, 619027185, 4334433953, 31240594737, 231398065115, 1758891930641, 13703162287733, 109302756028592] "" "Class ", 4043, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {4}, {[0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 5, 2], {5}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 423, 2086, 10858, 59040, 332995, 1938267, 11598734, 71143758, 446235219, 2856642931, 18634670617, 123702969885, 834711198128, 5719569462617, 39763955952970] "" "Class ", 4044, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {3, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1807, 8581, 41901, 209466, 1068880, 5556154, 29376298, 157800578, 860465547, 4759665741, 26693119204, 151706722323, 873423506464, 5092278000057] "" "Class ", 4045, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4046, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4047, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4048, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]} "Class ", 4049, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 461, 2457, 14159, 87296, 571194, 3941311, 28533126, 215827514, 1699913165, 13901624561, 117751685105, 1030912072081, 9311832438260, 86637798968259, 829115441889570] "" "Class ", 4050, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2082, 10922, 60478, 351615, 2137307, 13533630, 88985870, 605858133, 4261000895, 30891763208, 230460822868, 1766520357987, 13894391270483, 112011095959829] "" "Class ", 4051, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4052, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4053, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 3, 2, 5], {1, 3, 4}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 3, 2, 4], {3, 4}, {[0, 0, 1, 0, 0, 0]}], [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 1, 4, 3, 2], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[5, 2, 4, 3, 1], {2, 3, 4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 435, 2202, 11886, 67745, 404808, 2522582, 16325468, 109362273, 756245420, 5385840469, 39426364281, 296157829205, 2279368197031, 17950895987266, 144485766112391] "" "Class ", 4054, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4055, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2076, 10798, 58816, 333224, 1953860, 11811698, 73400220, 467746132, 3050717100, 20331354242, 138263235764, 958323863156, 6763014016044, 48551505630068] "" "Class ", 4056, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {3}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4057, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 410, 1978, 10126, 54726, 311271, 1859349, 11645610, 76371948, 523711535, 3750154060, 28002908013, 217741004209, 1760517766532, 14780386010861, 128667287517435] "" "Class ", 4058, " is:" {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 380, 1678, 7584, 34875, 162560, 766124, 3644066, 17469863, 84324840, 409471090, 1998933556, 9804748548, 48298256084, 238840150970, 1185256302910] "" "Class ", 4059, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 4060, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4061, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4062, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4063, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 4064, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 4065, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4066, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[1, 4, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4067, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4068, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4069, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4070, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4071, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4072, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4073, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4074, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4075, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4076, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4077, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4078, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4079, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4080, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4081, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4082, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4083, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4084, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 4085, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4086, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4087, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4088, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4089, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4090, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4091, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4092, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 4093, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4094, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4095, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4096, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4097, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4098, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4099, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4100, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4101, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4102, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4103, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4104, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4105, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4106, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4107, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[3, 2, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [0, 1, 1]]} "Class ", 4108, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4109, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4110, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4111, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4112, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {3}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {2, 3}, {}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {4}, {}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 4, 2], {4}, {[0, 0, 1, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 1991, 10225, 55218, 311734, 1832011, 11172863, 70551768, 460508191, 3103297971, 21571144642, 154556351354, 1140839690861, 8671218919788, 67836057691518] "" "Class ", 4113, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4114, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4115, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4116, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]} "Class ", 4117, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4118, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4119, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4120, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4121, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 4122, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 426, 2146, 11624, 67146, 411142, 2656052, 18035178, 128318314, 954086192, 7396278762, 59659032142, 499778527628, 4341025729290, 39035256389026, 362878164902216] "" "Class ", 4123, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182, 4412798, 33827974, 273646526, 2326980998, 20732504062, 192982729350, 1871953992254, 18880288847750, 197601208474238, 2142184050841734] "" "Class ", 4124, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 4125, " is:" {{[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4126, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 4127, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4128, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4129, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4130, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 4131, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 4132, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4133, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4134, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4135, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4136, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {4}, %1], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, %1], [[2, 1, 3, 4], {3}, %1], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, %1], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 2, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1}, {}], [[3, 4, 1, 2, 5], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 2, 4], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 2, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 2, 0]}]} %1 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4137, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4138, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4139, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4140, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4141, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4142, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4143, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4144, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4145, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4146, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4147, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 4148, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4149, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4150, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4151, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4152, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4153, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4154, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 4155, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4156, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4157, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4158, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4159, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4160, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4161, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4162, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4163, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4164, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4165, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4166, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}] , [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 0, 1]}], [[3, 4, 1, 2, 5], {1, 2, 4}, {}], [[3, 5, 1, 2, 4], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 366, 1552, 6652, 28696, 124310, 540040, 2350820, 10248248, 44725516, 195354368, 853829272, 3733693872, 16333556838, 71476391800, 312865382004] "" "Class ", 4167, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} "Class ", 4168, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4169, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4170, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4171, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 379, 1662, 7424, 33584, 153339, 705163, 3261676, 15159525, 70748333, 331359420, 1556869928, 7335480818, 34650355322, 164054807891, 778371387258] "" "Class ", 4172, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4173, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4174, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4175, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4176, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4177, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4178, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4179, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 4180, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4181, " is:" {{[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4182, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 102, 568, 3688, 27355, 228333, 2117678, 21604455, 240442666, 2898971487, 37640974533, 523649838707, 7770513437383, 122514483054534, 2045260957143682, 36040525971640131, 668513075034972294] "" "Class ", 4183, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 521, 3146, 21419, 162314, 1354813, 12349398, 122051734, 1299963907, 14843522837, 180878724534, 2342891649493, 32144076682709, 465662294097913, 7102990649343649, 113791688493695460] "" "Class ", 4184, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 2, 5], {2, 3}, {}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 1, 5, 2, 4], {2, 3}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}], [[4, 1, 5, 2, 3], {2, 3}, {}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3201, 22030, 168872, 1425987, 13146377, 131345368, 1413307424, 16291381270, 200252850871, 2614284072250, 36119509443701, 526478090984427, 8073234793660606, 129911048678309374] "" "Class ", 4185, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 491, 2790, 17498, 119696, 884525, 7007678, 59151215, 529200404, 4996080951, 49585010076, 515656325833, 5602918360055, 63447363599261, 747104828535846, 9129442103108202] "" "Class ", 4186, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 526, 3218, 22260, 171682, 1460249, 13575626, 136935959, 1489333042, 17372571847, 216334381367, 2864299318116, 40178293407905, 595203587115935, 9285514880534231, 152160249512382073] "" "Class ", 4187, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 4188, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 1, 3], {1}, {[0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[4, 3, 1, 2], {1}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2832, 17947, 124112, 927350, 7427885, 63373657, 572906005, 5463369687, 54751267598, 574727427044, 6301188098262, 71975135138339, 854617320009597, 10527439981057879] "" "Class ", 4189, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 4190, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 509, 3036, 20410, 152821, 1260344, 11352473, 110858506, 1166486436, 13155758239, 158306816606, 2024365198264, 27412701126669, 391852996666790, 5896336976076353, 93159929183835136] "" "Class ", 4191, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4192, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4193, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 495, 2877, 18759, 135627, 1077144, 9319655, 87256223, 878821164, 9474014775, 108841573040, 1327436936876, 17128376846674, 233122650860261, 3337627399416922, 50142971554766350] "" "Class ", 4194, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 463, 2492, 14574, 91544, 612258, 4330278, 32211795, 250895245, 2038622810, 17226019243, 150962216287, 1368909554516, 12817943135192, 123713438571246, 1228781053005792] "" "Class ", 4195, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4196, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4197, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 545, 3465, 25186, 205863, 1869772, 18680508, 203605930, 2404110787, 30570393023, 416496178234, 6052704720470, 93458149084548, 1527947331430913, 26368212094506240, 478993225721433793] "" "Class ", 4198, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 501, 2961, 19695, 145392, 1178992, 10414176, 99504794, 1022363219, 11238243476, 131586940514, 1634841616802, 21478826262169, 297511692083555, 4332907770980374, 66187588853680266] "" "Class ", 4199, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4200, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4201, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2950, 19598, 144602, 1172691, 10363748, 99109697, 1019532201, 11224218742, 131663104755, 1639248378892, 21588127900060, 299816162104266, 4379077471116009, 67101511723425051] "" "Class ", 4202, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4203, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4204, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4205, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 101, 556, 3572, 26231, 216700, 1989163, 20085036, 221239869, 2640073249, 33927597990, 467146946196, 6860924553984, 107063323329366, 1768977787066046, 30852128689629852, 566401354751051095] "" "Class ", 4206, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 522, 3159, 21575, 164088, 1375089, 12587100, 124941923, 1336617321, 15329605981, 187625865001, 2440911643285, 33633521067115, 489312591958616, 7494970363767367, 120564674227061019] "" "Class ", 4207, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4208, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4209, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3104, 21202, 161572, 1358658, 12494534, 124730288, 1343207518, 15520322620, 191523723392, 2513844304920, 34969174891314, 513894241860266, 7955349119465418, 129396171343586284] "" "Class ", 4210, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4211, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4212, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4213, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 532, 3306, 23336, 184253, 1609161, 15396452, 160153941, 1799267381, 21711097309, 280027635259, 3844417037293, 55971037461879, 861340163822531, 13969823246372312, 238159230777569482] "" "Class ", 4214, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 4215, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 4216, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3106, 21133, 160007, 1334359, 12151450, 119982767, 1276769903, 14566191746, 177357066241, 2295566408210, 31473070398058, 455650693210548, 6946172200371910, 111218471906470226] "" "Class ", 4217, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2742, 17127, 116399, 852251, 6670557, 55467941, 487534557, 4510356515, 43761630805, 443920775044, 4695400132153, 51660893726108, 590006654493170, 6981335107629933] "" "Class ", 4218, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 4219, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]} "Class ", 4220, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 542, 3426, 24742, 201044, 1815148, 18027370, 195317398, 2292511684, 28977885350, 392450611578, 5669334136110, 87017787752700, 1414189501395420, 24259859160588046, 438071839735618414] "" "Class ", 4221, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2924, 19221, 139948, 1118028, 9722332, 91417588, 924191162, 9995959040, 115174011280, 1408344044793, 18215107022185, 248441053987810, 3563819593622241, 53635684195891761] "" "Class ", 4222, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4223, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 467, 2552, 15232, 98051, 674441, 4921802, 37889753, 306274738, 2589407121, 22821918128, 209088408735, 1986360489596, 19525036614307, 198196104560082, 2074064524004087] "" "Class ", 4224, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2}, {}], [[1, 3, 4, 2], {1, 2}, {}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2891, 18906, 137056, 1090932, 9457319, 88699788, 894869865, 9663569017, 111219518613, 1359062162362, 17573098533569, 239716821895891, 3440433014837196, 51823676999967188] "" "Class ", 4225, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4226, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4227, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 0]]} "Class ", 4228, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 497, 2897, 18910, 136698, 1084329, 9366703, 87545605, 880362690, 9478610010, 108794805801, 1326156658164, 17109182779603, 232911758181029, 3336525435778820, 50172477611457334] "" "Class ", 4229, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4230, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4231, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {2, 3}, {}], [[4, 1, 3, 2, 5], {1, 2, 3}, {}], [[5, 1, 3, 2, 4], {2, 3}, {}], [[5, 1, 4, 2, 3], {2, 3}, {}], [[5, 1, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 3, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 512, 3068, 20724, 155750, 1288574, 11635145, 113838439, 1199576004, 13543405989, 163091660673, 2086525351579, 28261078284466, 403997128617802, 6078329040275630, 96010264015294153] "" "Class ", 4232, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2540, 15126, 97262, 669159, 4890540, 37751947, 306362728, 2603458041, 23091113192, 213148974500, 2042641702140, 20278194783305, 208142332182874, 2205167767929616] "" "Class ", 4233, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4234, " is:" {{[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4235, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[1, 4, 3, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4236, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 3, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 556, 3330, 22244, 163766, 1317073, 11487391, 107997283, 1088807468, 11719132222, 134136642788, 1627057797022, 20850576731743, 281503859511044, 3994002943888366, 59414962905936847] "" "Class ", 4237, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[4, 1, 2, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4238, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 527, 3229, 22366, 172666, 1469718, 13671711, 137971821, 1501212378, 17517310235, 218204099271, 2889844692231, 40546531246916, 600790797457660, 9374545291470197, 153647029035681397] "" "Class ", 4239, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2739, 17388, 121952, 936937, 7826457, 70635044, 685038810, 7105289563, 78488576628, 919987827155, 11404506138130, 149075745073530, 2049359001955135, 29557229417672001] "" "Class ", 4240, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2765, 17647, 124394, 959728, 8043349, 72760192, 706560608, 7330733846, 80926122566, 947077371475, 11711855704692, 152597027658021, 2089341170839114, 29990703584466363] "" "Class ", 4241, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}], [ [2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 452, 2403, 13949, 87592, 590757, 4254111, 32546959, 263431902, 2247383588, 20143142381, 189134135807, 1855631319300, 18979875966980, 201963834308827, 2231595040542684] "" "Class ", 4242, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4243, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4244, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4245, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4246, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2534, 15151, 98426, 689349, 5173207, 41386570, 351431126, 3155428158, 29857596953, 296847683551, 3092645160734, 33681916710307, 382637051026218, 4525253065218889] "" "Class ", 4247, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4248, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4249, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4250, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4251, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4252, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2943, 19462, 142846, 1152527, 10139817, 96612695, 991102828, 10891385956, 127645327762, 1589246103743, 20947932358515, 291417855722200, 4266920741853107, 65592180870539323] "" "Class ", 4253, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2468, 14710, 95562, 670988, 5056920, 40670280, 347338320, 3136772116, 29845742664, 298238193182, 3121048946778, 34119674096412, 388777200157152, 4607973479432672] "" "Class ", 4254, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4255, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4256, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4257, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4258, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4259, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4260, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 515, 3109, 21206, 161286, 1353284, 12417910, 123702978, 1329453039, 15331970873, 188856547551, 2474588674688, 34367308321357, 504274295993115, 7795067869127705, 126613958281574438] "" "Class ", 4261, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 96, 485, 2775, 17738, 125282, 968876, 8143928, 73933759, 720986214, 7516797523, 83436505123, 982427481778, 12230546253544, 160516626252072, 2215018043289873, 32061260202339667] "" "Class ", 4262, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4263, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4264, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4265, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4266, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4267, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4268, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 486, 2797, 18057, 129170, 1014437, 8675915, 80264653, 798638333, 8504146175, 96490628792, 1162133051285, 14807272396689, 198990605689297, 2812883394189712, 41722496728142436] "" "Class ", 4269, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4270, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4271, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4272, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4273, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4274, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2912, 19099, 138840, 1108077, 9632761, 90608115, 916934673, 9933721732, 114710714176, 1406542131754, 18250853722354, 249848896984857, 3598747785933909, 54404590508210586] "" "Class ", 4275, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2449, 14464, 92792, 641463, 4747005, 37400326, 312262490, 2751816419, 25507591805, 247942722780, 2520578611104, 26734932704761, 295228704051667, 3387668284755909] "" "Class ", 4276, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2435, 14304, 91095, 623840, 4564035, 35478818, 291713508, 2527111261, 22988782741, 218957862220, 2177907955100, 22571512170050, 243241491151290, 2720657540807660] "" "Class ", 4277, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2131, 11449, 65297, 392486, 2472338, 16246576, 110957646, 785109389, 5740147551, 43265436029, 335521492233, 2672413718104, 21828412595376, 182591440966276] "" "Class ", 4278, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4279, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4280, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4281, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 0]]} "Class ", 4282, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4283, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4284, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2576, 15613, 103067, 734699, 5616698, 45786575, 396087255, 3621039385, 34858152669, 352236363369, 3725765700034, 41150598250802, 473541708790633, 5666323086864736] "" "Class ", 4285, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2116, 11304, 64132, 383999, 2414201, 15868079, 108641161, 772402845, 5687785004, 43284664641, 339777536855, 2746696789908, 22832498041193, 194923046415994] "" "Class ", 4286, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]} "Class ", 4287, " is:" {{[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4288, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4289, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 4290, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4291, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4292, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4293, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4294, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4295, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4296, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4297, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4298, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4299, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4300, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4301, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4302, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4303, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 4304, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4305, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4306, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4307, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4308, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4309, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4310, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4311, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 4312, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4313, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4314, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4315, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4316, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4317, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4318, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4319, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4320, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4321, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4322, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4323, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4324, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4325, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4326, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4327, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4328, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4329, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4330, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4331, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 0]]} "Class ", 4332, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4333, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]} "Class ", 4334, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 4335, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4336, " is:" {{[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4337, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4338, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4339, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[4, 1, 2, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4340, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4341, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4342, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4343, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4344, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4345, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4346, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4347, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4348, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4349, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4350, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4351, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4352, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 4353, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4354, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4355, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4356, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4357, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4358, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4359, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4360, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 4361, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4362, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4363, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4364, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4365, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4366, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4367, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4368, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4369, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4370, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4371, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4372, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4373, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4374, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4375, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 2, 0, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {3}, %1], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {3}, %1], [[2, 4, 3, 1], {3}, %1], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, %1]} %1 := {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 381, 1692, 7708, 35769, 168300, 800365, 3838242, 18530836, 89957026, 438670927, 2147258093, 10544273864, 51919690991, 256250661394, 1267300564458] "" "Class ", 4376, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4377, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4378, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4379, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 0]]} "Class ", 4380, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4381, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4382, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]} "Class ", 4383, " is:" {{[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}} {[[1, 4, 3, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4384, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 100, 537, 3328, 23361, 183216, 1587528, 15059120, 155206353, 1726904364, 20629917997, 263351198863, 3577505684904, 51528029924261, 784356223199969, 12581346268848636, 212103979670291157] "" "Class ", 4385, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 493, 2841, 18295, 130248, 1016435, 8631306, 79262434, 782873048, 8276987516, 93276826714, 1116244370207, 14137295182684, 188921488349849, 2656560910798362, 39211104059674020] "" "Class ", 4386, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {4}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {3}, {}], [[1, 4, 2, 5, 3], {3, 4}, {}], [[1, 4, 3, 5, 2], {3, 4}, {}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3}, {}], [[3, 1, 4, 2, 5], {3, 4}, {}], [[3, 1, 5, 2, 4], {3, 4}, {}], [[4, 1, 5, 2, 3], {3, 4}, {}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 499, 2932, 19357, 141857, 1142699, 10036476, 95468397, 977832195, 10730826036, 125625359213, 1562898600351, 20592644335676, 286480163135854, 4196456805188059, 64564524077104080] "" "Class ", 4387, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {[0, 0, 0, 0, 1, 0]}], [[1, 5, 2, 3, 4], {3}, {}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2529, 15064, 97300, 676360, 5029732, 39817528, 334150488, 2961769907, 27636197861, 270668988977, 2775009502404, 29709188722249, 331392773985149, 3843518204591319] "" "Class ", 4388, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 496, 2886, 18815, 135778, 1074419, 9248798, 86041351, 860195031, 9196997115, 104717141500, 1265007280500, 16159777917911, 217651138144783, 3082584546952894, 45798745089392490] "" "Class ", 4389, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 4390, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2580, 15679, 103847, 742866, 5697503, 46567858, 403560161, 3692086357, 35527008073, 358393548607, 3779545563664, 41562525360420, 475522596768476, 5649001855404841] "" "Class ", 4391, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 4392, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 4393, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 439, 2265, 12595, 74716, 469187, 3100198, 21450742, 154807424, 1161463755, 9033878734, 72670593016, 603336049936, 5160448077425, 45399099782563, 410222222945582] "" "Class ", 4394, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 4395, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 513, 3085, 20945, 158313, 1318271, 11987081, 118169601, 1255163218, 14289188611, 173556782898, 2240088889002, 30615793035425, 441691595074510, 6707580616471551, 106951539234693627] "" "Class ", 4396, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2614, 16119, 108963, 800269, 6338455, 53806457, 486980117, 4677966529, 47508763750, 508360843046, 5713954104819, 67281725629669, 827951845963051, 10624702355583537] "" "Class ", 4397, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4398, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4399, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 95, 469, 2598, 15913, 106575, 773453, 6038412, 50407591, 447658030, 4211033494, 41801591276, 436449518106, 4779206389198, 54744594494267, 654471638717930, 8149004246130081] "" "Class ", 4400, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4401, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4402, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4403, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1}, {}], [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 99, 525, 3208, 22188, 171252, 1459110, 13599689, 137634153, 1502916962, 17611887645, 220447683091, 2935306698381, 41426634191131, 617714738523027, 9703516521496669, 160169049598475204] "" "Class ", 4404, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2852, 18391, 130957, 1020544, 8639698, 78964986, 775070703, 8132511181, 90852414236, 1076784428218, 13496445396493, 178388173422963, 2479964208135603, 36177332748712055] "" "Class ", 4405, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4406, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4407, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 484, 2768, 17712, 125400, 973488, 8223880, 75116680, 737741056, 7753302432, 86825816384, 1032208763680, 12983680635040, 172284211349632, 2405164117757920, 35240342998767968] "" "Class ", 4408, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4409, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4410, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4411, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 4412, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 455, 2451, 14497, 93204, 646026, 4794894, 37890263, 317221324, 2801818750, 26010987743, 252992833957, 2570731154031, 27221092950467, 299693800379290, 3423717330177799] "" "Class ", 4413, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]} "Class ", 4414, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 510, 3042, 20418, 152298, 1248772, 11160812, 107942966, 1122985658, 12502290114, 148288693814, 1866533445990, 24847452998990, 348754699200696, 5147120649804096, 79679512372977758] "" "Class ", 4415, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2577, 15639, 103448, 739633, 5676578, 46502272, 404657023, 3725067515, 36145767844, 368544122877, 3937501555657, 43971679476373, 512129957398402, 6208272721259367] "" "Class ", 4416, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[1, 0, 0, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {2}, {[1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {[1, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2586, 15801, 105676, 766985, 6000046, 50298418, 449640933, 4268214018, 42864603230, 453955066343, 5055223388875, 59042313201958, 721569211882306, 9208204592353934] "" "Class ", 4417, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {3, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {2, 3}, {}], [[1, 2, 5, 3, 4], {2, 3}, {}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 4, 1], {3, 4, 5}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {2, 3, 5}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 438, 2257, 12555, 74669, 471151, 3135107, 21890216, 159722541, 1213625622, 9574466805, 78223455210, 660354963327, 5748800008154, 51519968938193, 474562281222125] "" "Class ", 4418, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 465, 2534, 15140, 98182, 685356, 5117026, 40646873, 342006988, 3036696203, 28360196596, 277787339541, 2846464358605, 30443856226579, 339158243200974, 3928306951732838] "" "Class ", 4419, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 4420, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3, 4, 5}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 436, 2229, 12260, 71905, 446395, 2917010, 19969317, 142666335, 1060165998, 8171444782, 65167114958, 536577802477, 4552885283591, 39742862746225, 356363980506876] "" "Class ", 4421, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[3, 2, 1, 4], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 0, 1]]} "Class ", 4422, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 437, 2237, 12297, 71879, 443390, 2869725, 19396979, 136401144, 994736593, 7503009058, 58397325491, 468065750737, 3856641906943, 32615299210241, 282707427418088] "" "Class ", 4423, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4424, " is:" {{[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4425, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[4, 1, 2, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[1, 4, 3, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 4426, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 494, 2825, 17811, 122176, 902786, 7130308, 59820538, 530385853, 4948564622, 48410437206, 495014997007, 5276436624591, 58488809771113, 672820525209345, 8016840243116836] "" "Class ", 4427, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 452, 2396, 13821, 85913, 571351, 4042158, 30281232, 239276072, 1987686787, 17308514908, 157586968516, 1496691321759, 14797741926244, 152016907510093, 1619847599323231] "" "Class ", 4428, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2460, 14544, 93224, 642384, 4726360, 36922736, 304832688, 2649109376, 24150115264, 230262171488, 2290183874848, 23705693525376, 254840434430784, 2839932014269184] "" "Class ", 4429, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2108, 11154, 62252, 364190, 2223393, 14119106, 93037135, 635002005, 4482846404, 32696836304, 246164136110, 1911414141780, 15295599340933, 126049648339545] "" "Class ", 4430, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 4431, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 4432, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 4433, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 4434, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 4435, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 4436, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 468, 2568, 15433, 100363, 700053, 5201196, 40930485, 339586999, 2958951221, 26988665050, 256951701275, 2547265363067, 26236347245903, 280219442661749, 3098173868016989] "" "Class ", 4437, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 425, 2127, 11382, 64520, 384772, 2401346, 15618563, 105512083, 738302103, 5338594346, 39812638817, 305685535675, 2412915479720, 19554782726800, 162517911410784] "" "Class ", 4438, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4439, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4440, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4441, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4442, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4443, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4444, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 482, 2707, 16725, 112280, 811264, 6262312, 51336341, 444726973, 4054573303, 38765822514, 387509728073, 4039159877321, 43798171031016, 493028602042206, 5750807969031498] "" "Class ", 4445, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {1}, {[0, 1, 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, 6, 22, 94, 455, 2435, 14202, 89382, 602168, 4315995, 32750357, 262025127, 2202711552, 19398579402, 178504996728, 1712375262872, 17089209148625, 177097880884141, 1902570854855311] "" "Class ", 4446, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4447, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4448, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4449, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4450, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4451, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4452, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 91, 411, 1995, 10315, 56485, 326276, 1982049, 12632103, 84291144, 587814665, 4276769268, 32412383341, 255480463449, 2091288908520, 17752700927913, 156070596693390] "" "Class ", 4453, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]} "Class ", 4454, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2536, 15070, 96637, 662771, 4827394, 37131319, 300216859, 2541653332, 22457353114, 206507447367, 1971430315301, 19496607777935, 199360375436145, 2104167235840654] "" "Class ", 4455, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2112, 11220, 62972, 370740, 2277048, 14526496, 95917728, 653607872, 4585130952, 33044378440, 244217436016, 1848045892544, 14299233218000, 112993176598128] "" "Class ", 4456, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {}], [[2, 3, 1, 5, 4], {1, 2, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 4, 1, 3, 5], {1, 2}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4], {1, 2}, {}], [[2, 5, 1, 4, 3], {1, 2, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 4, 2], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 427, 2155, 11676, 67248, 408732, 2606438, 17357456, 120250730, 863890823, 6418238225, 49197282385, 388285171409, 3149704199501, 26218804660825, 223650631923572] "" "Class ", 4457, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, %1], [[1, 3, 4, 2], {2, 3}, %1], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {3, 4}, %1], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, %1]} %1 := {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 398, 1874, 9310, 48482, 263326, 1485794, 8680830, 52374658, 325564766, 2080889250, 13652344190, 91802512770, 631841980126, 4445791626786, 31945484268798] "" "Class ", 4458, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 4459, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 4460, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} "Class ", 4461, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[3, 2, 1, 4], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[1, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [ [2, 1, 3, 4], {3, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[1, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 368, 1582, 6934, 30838, 138722, 629806, 2881210, 13265564, 61412108, 285653482, 1334210890, 6254579072, 29416135712, 138752409354, 656203613626] "" "Class ", 4462, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}], [[3, 1, 4, 2], {}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}], [[3, 1, 4, 2, 5], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 2, 4}, {[0, 0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 398, 1870, 9229, 47469, 253034, 1392069, 7879112, 45766170, 272264418, 1656155642, 10286756470, 65165349100, 420611092345, 2763702497669, 18472012535825] "" "Class ", 4463, " is:" {{[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 365, 1539, 6545, 27977, 119991, 515837, 2221343, 9577949, 41338378, 178552008, 771679954, 3336711586, 14433413888, 62453572080, 270307952600] "" "Class ", 4464, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4465, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4466, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4467, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4468, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4469, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4470, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 443, 2337, 13472, 84007, 562136, 4010411, 30340183, 242304158, 2034881098, 17910414804, 164740255197, 1579474153894, 15749296385040, 162992693531721, 1747611971719874] "" "Class ", 4471, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4472, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4473, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 4474, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4475, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4476, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4477, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4478, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4479, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4480, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4481, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 4482, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4483, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4484, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4485, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4486, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4487, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4488, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4489, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]} "Class ", 4490, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4491, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4492, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4493, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {2}, {}], [[1, 3, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {3}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 2, 4, 3, 5], {2, 3}, {}], [[1, 2, 5, 3, 4], {2}, {}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 2, 5], {2, 3}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2}, {[0, 0, 1, 0, 0, 0]}], [[1, 3, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 3, 5], {2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 3, 4], {3}, {}], [[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, 3, 5, 4, 1], {1, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 4, 5, 3, 1], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {3, 4}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 397, 1856, 9090, 46248, 242907, 1310782, 7240271, 40817184, 234302956, 1366889603, 8091566577, 48541596468, 294787475207, 1810603355722, 11238891884836] "" "Class ", 4494, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4495, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4496, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4497, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[3, 2, 1, 4], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [0, 1, 1]]} "Class ", 4498, " is:" {{[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4499, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4500, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4501, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4502, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1}, {[0, 1, 0, 0, 0]}], [[4, 2, 3, 1], {1}, {}], [[2, 4, 1, 3, 5], {1, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 2, 5], {1, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[4, 5, 1, 2, 3], {4}, {}], [[4, 5, 1, 3, 2], {1, 2}, {[0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 395, 1823, 8741, 43192, 218677, 1129519, 5932605, 31603937, 170408865, 928500329, 5105360024, 28297178891, 157954119674, 887263190868, 5012123024566] "" "Class ", 4503, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4504, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4505, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4506, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 4, 1, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "Class ", 4507, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 0, 2, 0], [0, 1, 0, 0]}], [[2, 1, 3], {1}, {[0, 2, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 2, 0]}], [[3, 1, 2], {1}, {[0, 0, 1, 0], [0, 2, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 87382, 349526, 1398102, 5592406, 22369622, 89478486, 357913942, 1431655766, 5726623062, 22906492246, 91625968982] "" "Class ", 4508, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "Class ", 4509, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4510, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4511, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {[0, 1, 1, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 381, 1694, 7744, 36168, 171831, 827814, 4034589, 19857262, 98555324, 492710856, 2478897620, 12541604830, 63768192378, 325674039636, 1669922290311] "" "Class ", 4512, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4513, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4514, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4515, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "Class ", 4516, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4517, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4518, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4519, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4520, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4521, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4522, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 4523, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 4524, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 4525, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {[0, 2, 0, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {[0, 0, 2, 0, 0], [0, 1, 1, 0, 0], [0, 2, 0, 0, 0]}], [[1, 2, 4, 3], {1}, %1], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1}, %1], [[1, 4, 2, 3], {3}, %1], [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1}, %1], [[2, 4, 1, 3], {3}, %1], [[2, 4, 3, 1], {3}, %1], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, %1]} %1 := {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 368, 1582, 6934, 30838, 138722, 629806, 2881210, 13265564, 61412108, 285653482, 1334210890, 6254579072, 29416135712, 138752409354, 656203613626] "" "Class ", 4526, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 4527, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 4528, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 4529, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} "Class ", 4530, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 500, 2947, 19545, 143954, 1165433, 10283756, 98211550, 1009107723, 11098357469, 130077896040, 1618404524350, 21302033815537, 295720010306481, 4317963938436727, 66152489036083904] "" "Class ", 4531, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [0, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4532, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3107, 21270, 162583, 1372017, 12666266, 126959310, 1372934516, 15931166307, 197432290042, 2602428122048, 36354428254779, 536484912075080, 8339317383970895, 136192348695271197] "" "Class ", 4533, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4534, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {[0, 1, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 97, 498, 2916, 19170, 139744, 1118631, 9753271, 92001519, 933498138, 10137883294, 117331328750, 1441641268090, 18741699460572, 257014948266367, 3707900879972029, 56137708547972309] "" "Class ", 4535, " is:" {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {1, 2}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {}], [[3, 2, 4, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 466, 2542, 15191, 98301, 682637, 5051093, 39595875, 327276498, 2840751917, 25805257068, 244591401657, 2412659409600, 24709835707098, 262223235444292, 2878074927063529] "" "Class ", 4536, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 1, 4, 3], [1, 0, 0]]} "Class ", 4537, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}, {[[3, 4, 1, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 0]]} "Class ", 4538, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 509, 3018, 20087, 148313, 1203065, 10635201, 101765009, 1047925966, 11554958941, 135835248353, 1695862624548, 22408868038461, 312446978205693, 4584276069593353, 70604008565930651] "" "Class ", 4539, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 95, 470, 2616, 16159, 109627, 810148, 6477205, 55702567, 512698093, 5028759416, 52361675717, 576831699658, 6702779697833, 81931745567211, 1050936451945664, 14114377686084488] "" "Class ", 4540, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4541, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4542, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4543, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4544, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4545, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4546, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 514, 3102, 21173, 161201, 1354193, 12440927, 124071201, 1334804383, 15408540687, 189968414424, 2491193104409, 34623961168091, 508392831705299, 7863770052464830, 127805647229439900] "" "Class ", 4547, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 487, 2823, 18455, 134510, 1082392, 9536242, 91331303, 944998941, 10507179879, 124953732786, 1582803928826, 21277883184519, 302574456833555, 4537983650379768, 71592767060398068] "" "Class ", 4548, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4549, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4550, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4551, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4552, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4553, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4554, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {}], [ [3, 4, 2, 1, 5], {1, 2, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 454, 2433, 14277, 90826, 621511, 4545327, 35337861, 290743957, 2521709068, 22979291663, 219362412927, 2188005167411, 22750777800153, 246100014081567, 2764322618995457] "" "Class ", 4555, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 424, 2119, 11370, 65032, 394155, 2518808, 16898045, 118573216, 867505133, 6599497753, 52080653990, 425468431586, 3591570996581, 31276154935987, 280550583934141] "" "Class ", 4556, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]} "Class ", 4557, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]} "Class ", 4558, " is:" {{[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}} {[[2, 1, 4, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]} "Class ", 4559, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 4, 5, 1], {2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 458, 2500, 15064, 99037, 704066, 5373985, 43782533, 378860913, 3467336309, 33439572417, 338756092134, 3594622228416, 39854167596150, 460656786913217, 5539749669686295] "" "Class ", 4560, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4561, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4562, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4563, " is:" {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}], [[3, 1, 4, 2], {3}, {}], [[3, 2, 4, 1], {}, {[0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 4, 1, 5], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 4, 5, 1], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 2, 5, 1, 3], {2, 3}, {[0, 1, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 3, 5, 2, 1], {1}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 92, 422, 2080, 10884, 59984, 346186, 2082948, 13018920, 84273374, 563521205, 3883940527, 27538352087, 200524637796, 1497293866164, 11449101432823, 89543925178321] "" "Class ", 4564, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 1, 4, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 1, 4, 3], [1, 1, 0]]} "Class ", 4565, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2692, 16536, 110175, 789285, 6036596, 49005496, 420267468, 3792260404, 35881734445, 354944656137, 3661257051432, 39290252142317, 437760324378009, 5054621776961360] "" "Class ", 4566, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 93, 442, 2319, 13237, 81286, 532455, 3695900, 27040644, 207616218, 1666642807, 13944009117, 121258780713, 1093424387314, 10202551302156, 98326568473636, 977144789151375] "" "Class ", 4567, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 0]]} "Class ", 4568, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4569, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 0, 1]]} "Class ", 4570, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 0, 1]]} "Class ", 4571, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [0, 1, 1]]} "Class ", 4572, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[2, 4, 1, 3], [1, 1, 1]]} "Class ", 4573, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 96, 481, 2702, 16739, 112978, 823065, 6424191, 53395408, 470204254, 4368164128, 42651842871, 436325952504, 4663353419809, 51942260697869, 601613924637290, 7231498214809526] "" "Class ", 4574, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}], [[3, 1, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}], [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 94, 456, 2463, 14612, 94227, 654992, 4874597, 38621288, 324205702, 2871691606, 26744402713, 261067798256, 2663821233105, 28341747455790, 313738532399833, 3606396930456404] "" "Class ", 4575, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]} "Class ", 4576, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4577, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "Class ", 4578, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4579, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} "Class ", 4580, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4581, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 4, 1, 2], [1, 1, 0]]} "Class ", 4582, " is:" {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1, 5], {1, 2}, { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 1, 4], {1, 2}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1], {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 364, 1526, 6439, 27281, 115961, 494325, 2112802, 9052336, 38871537, 167258719, 721030311, 3113535169, 13465545118, 58318321194, 252897316844] "" "Class ", 4583, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4584, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4585, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4586, " is:" {{[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4587, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4588, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4589, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4590, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4591, " is:" {{[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4592, " is:" {{[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]} "For the class ", {{[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ", {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 98, 511, 3052, 20523, 153382, 1260814, 11301721, 109687509, 1145719264, 12813663713, 152758246654, 1933638182575, 25899212101465, 365936407676696, 5439241978941500, 84841616509800931] "" "Class ", 4593, " is:" {{[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [0, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4594, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 1, 3], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4595, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 0]]} "Class ", 4596, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4597, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4598, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 0, 1]]} "Class ", 4599, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]} "Class ", 4600, " is:" {{[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}} {[[2, 4, 1, 3], [0, 0, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 0, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4601, " is:" {{[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [0, 1, 1]]} {[[2, 4, 1, 3], [0, 1, 0]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4602, " is:" {{[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[3, 1, 4, 2], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[2, 4, 1, 3], [0, 1, 1]], [[2, 4, 1, 3], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[2, 4, 1, 3], [1, 1, 0]]} "Class ", 4603, " is:" {{[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 0, 1]]} {[[2, 4, 1, 3], [1, 0, 1]], [[3, 1, 4, 2], [1, 1, 0]]} "Class ", 4604, " is:" {{[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}} {[[2, 4, 1, 3], [0, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 0]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4605, " is:" {{%2, [[1, 3, 4, 2], [1, 1, 1]]}, {%2, [[1, 4, 2, 3], [1, 1, 1]]}, {%2, [[2, 3, 1, 4], [1, 1, 1]]}, {%2, [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], %1}, {[[3, 2, 4, 1], [1, 1, 1]], %1}, {[[4, 1, 3, 2], [1, 1, 1]], %1}, {[[4, 2, 1, 3], [1, 1, 1]], %1}} %1 := [[4, 3, 2, 1], [1, 1, 1]] %2 := [[1, 2, 3, 4], [1, 1, 1]] {[[1, 2, 3, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]} "For the class ", {{%1, [[1, 3, 4, 2], [1, 1, 1]]}, {%1, [[1, 4, 2, 3], [1, 1, 1]]}, {%1, [[2, 3, 1, 4], [1, 1, 1]]}, {%1, [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], %2}, {[[3, 2, 4, 1], [1, 1, 1]], %2}, {[[4, 1, 3, 2], [1, 1, 1]], %2}, {[[4, 2, 1, 3], [1, 1, 1]], %2}}, " the pattern set ", {%1, [[1, 3, 4, 2], [1, 1, 1]]}, " has scheme:" %1 := [[1, 2, 3, 4], [1, 1, 1]] %2 := [[4, 3, 2, 1], [1, 1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 1]}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 1]}], [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 1]}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 89, 380, 1678, 7584, 34875, 162560, 766124, 3644066, 17469863, 84324840, 409471090, 1998933556, 9804748548, 48298256084, 238840150970, 1185256302910] "" "Class ", 4606, " is:" {{%2, [[2, 4, 3, 1], [1, 1, 1]]}, {%2, [[3, 2, 4, 1], [1, 1, 1]]}, {%2, [[4, 1, 3, 2], [1, 1, 1]]}, {%2, [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], %1}, {[[1, 4, 2, 3], [1, 1, 1]], %1}, {[[2, 3, 1, 4], [1, 1, 1]], %1}, {[[3, 1, 2, 4], [1, 1, 1]], %1}} %1 := [[4, 3, 2, 1], [1, 1, 1]] %2 := [[1, 2, 3, 4], [1, 1, 1]] {[[1, 2, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[1, 2, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 4607, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[4, 1, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[4, 2, 1, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4608, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[3, 4, 2, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {3}, {[0, 0, 0, 1]}], [[2, 3, 1], {2}, {[0, 0, 1, 1]}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 4}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 2, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 1]}], [[2, 4, 3, 1], {2, 3}, {[0, 0, 0, 1, 1], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0]}] , [[3, 1, 2, 4], {2, 4}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {[0, 0, 1, 0, 1], [0, 0, 1, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 367, 1571, 6861, 30468, 137229, 625573, 2881230, 13388094, 62688448, 295504025, 1401195334, 6678877732, 31984089193, 153809536017, 742462191363] "" "Class ", 4609, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {[0, 0, 2, 0]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, %3], [[1, 4, 2, 3], {2, 3}, %3], [[1, 4, 3, 2], {3}, {[0, 0, 0, 2, 0], [0, 0, 1, 1, 0], [0, 0, 2, 0, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 0, 2, 0]}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {}, {[0, 0, 0, 2, 0]}], [[3, 1, 2, 4], {3}, %3], [[3, 1, 4, 2], {}, {[0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1}, %3], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, %3], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {3, 4}, %2], [[2, 1, 5, 3, 4], {3, 4}, %2], [[2, 1, 5, 4, 3], {4}, {[0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}], [[2, 4, 3, 1, 5], {1, 2}, %2], [[2, 5, 3, 1, 4], {1, 2}, %2], [[2, 5, 4, 1, 3], {1, 2}, %2], [[3, 1, 4, 2, 5], {3, 4}, %1], [[3, 1, 5, 2, 4], {3, 4}, %1], [[3, 1, 5, 4, 2], {4}, {[0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1}, {[0, 0, 0, 0, 2, 0]}], [[3, 5, 4, 1, 2], {1, 2}, %1], [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 2, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {[0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1}, {[0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0]}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %2 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} %3 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 365, 1540, 6568, 28269, 122752, 537708, 2375500, 10579400, 47469377, 214454528, 974870969, 4456401809, 20474068387, 94490731125, 437872264778] "" "Class ", 4610, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], %2}, {[[1, 2, 4, 3], [1, 1, 1]], %1}, {[[2, 1, 3, 4], [1, 1, 1]], %2}, {[[2, 1, 3, 4], [1, 1, 1]], %1}, {%2, [[3, 4, 2, 1], [1, 1, 1]]}, {%2, [[4, 3, 1, 2], [1, 1, 1]]}, {%1, [[3, 4, 2, 1], [1, 1, 1]]}, {%1, [[4, 3, 1, 2], [1, 1, 1]]}} %1 := [[3, 1, 4, 2], [1, 1, 1]] %2 := [[2, 4, 1, 3], [1, 1, 1]] {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 1, 3, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Class ", 4611, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[3, 1, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[2, 4, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [2, 5, 3, 1, 4], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1}, {}], [[3, 5, 4, 1, 2], {1, 3}, {[0, 1, 0, 0, 0, 0]}], [[3, 5, 4, 2, 1], {4}, {}], [[4, 2, 3, 1, 5], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [ [5, 2, 3, 1, 4], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 3, 4, 1, 2], {2, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[5, 3, 4, 2, 1], {4}, {[0, 0, 0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 363, 1507, 6241, 25721, 105485, 430767, 1752945, 7113095, 28797292, 116368938, 469531170, 1892133076, 7617145998, 30638026074, 123145086046] "" "Class ", 4612, " is:" {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}} {[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]} "For the class ", {{[[1, 2, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 1, 3, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[1, 3, 2, 4], {2, 3}, %1], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1}, {}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 1, 0]}], [[3, 1, 2, 4], {3}, %1], [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1}, {}], [[3, 4, 2, 1], {3}, %1], [[4, 1, 2, 3], {3}, {[0, 0, 1, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0]}], [[4, 2, 3, 1], {1}, %1], [[2, 1, 4, 3, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 1, 4, 2, 5], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 2, 4], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}], [[3, 2, 5, 4, 1], {1, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 0]}], [[4, 1, 5, 3, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 2, 5, 3, 1], {1, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]} %1 := {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 337, 1299, 4910, 18228, 66640, 240550, 859295, 3043525, 10705182, 37441618, 130351650, 452119862, 1563402141, 5392828631, 18564966510] "" "Class ", 4613, " is:" {{%2, [[1, 3, 4, 2], [1, 1, 1]]}, {%2, [[1, 4, 2, 3], [1, 1, 1]]}, {%2, [[2, 3, 1, 4], [1, 1, 1]]}, {%2, [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], %1}, {[[3, 2, 4, 1], [1, 1, 1]], %1}, {[[4, 1, 3, 2], [1, 1, 1]], %1}, {[[4, 2, 1, 3], [1, 1, 1]], %1}} %1 := [[4, 2, 3, 1], [1, 1, 1]] %2 := [[1, 3, 2, 4], [1, 1, 1]] {[[1, 3, 2, 4], [1, 1, 1]], [[1, 3, 4, 2], [1, 1, 1]]} "For the class ", {{%1, [[1, 3, 4, 2], [1, 1, 1]]}, {%1, [[1, 4, 2, 3], [1, 1, 1]]}, {%1, [[2, 3, 1, 4], [1, 1, 1]]}, {%1, [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], %2}, {[[3, 2, 4, 1], [1, 1, 1]], %2}, {[[4, 1, 3, 2], [1, 1, 1]], %2}, {[[4, 2, 1, 3], [1, 1, 1]], %2}}, " the pattern set ", {%1, [[1, 3, 4, 2], [1, 1, 1]]}, " has scheme:" %1 := [[1, 3, 2, 4], [1, 1, 1]] %2 := [[4, 2, 3, 1], [1, 1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 1, 1]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4614, " is:" {{%2, [[2, 4, 3, 1], [1, 1, 1]]}, {%2, [[3, 2, 4, 1], [1, 1, 1]]}, {%2, [[4, 1, 3, 2], [1, 1, 1]]}, {%2, [[4, 2, 1, 3], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], %1}, {[[1, 4, 2, 3], [1, 1, 1]], %1}, {[[2, 3, 1, 4], [1, 1, 1]], %1}, {[[3, 1, 2, 4], [1, 1, 1]], %1}} %1 := [[4, 2, 3, 1], [1, 1, 1]] %2 := [[1, 3, 2, 4], [1, 1, 1]] {[[1, 3, 2, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} {[[1, 3, 2, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]} "Class ", 4615, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[4, 1, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 2, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4616, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], %2}, {[[1, 4, 2, 3], [1, 1, 1]], %2}, {%2, [[2, 3, 1, 4], [1, 1, 1]]}, {%2, [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], %1}, {[[3, 2, 4, 1], [1, 1, 1]], %1}, {%1, [[4, 1, 3, 2], [1, 1, 1]]}, {%1, [[4, 2, 1, 3], [1, 1, 1]]}} %1 := [[3, 4, 1, 2], [1, 1, 1]] %2 := [[2, 1, 4, 3], [1, 1, 1]] {[[1, 3, 4, 2], [1, 1, 1]], [[2, 1, 4, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], %1}, {[[1, 4, 2, 3], [1, 1, 1]], %1}, {%1, [[2, 3, 1, 4], [1, 1, 1]]}, {%1, [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], %2}, {[[3, 2, 4, 1], [1, 1, 1]], %2}, {%2, [[4, 1, 3, 2], [1, 1, 1]]}, {%2, [[4, 2, 1, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 1, 1]], %1}, " has scheme:" %1 := [[2, 1, 4, 3], [1, 1, 1]] %2 := [[3, 4, 1, 2], [1, 1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[1, 4, 2, 3], {3}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 1, 3, 4], {3, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}] , [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2, 3}, {}], [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}], [[4, 2, 3, 1], {1, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 368, 1584, 6968, 31192, 141656, 651136, 3023840, 14166496, 66876096, 317809216, 1519163456, 7299577216, 35237444736, 170812433536, 831127053696] "" "Class ", 4617, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4618, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], %2}, {[[1, 4, 2, 3], [1, 1, 1]], %1}, {[[2, 3, 1, 4], [1, 1, 1]], %1}, {%2, [[3, 1, 2, 4], [1, 1, 1]]}, {%2, [[3, 2, 4, 1], [1, 1, 1]]}, {%2, [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], %1}, {%1, [[4, 2, 1, 3], [1, 1, 1]]}} %1 := [[3, 1, 4, 2], [1, 1, 1]] %2 := [[2, 4, 1, 3], [1, 1, 1]] {[[1, 3, 4, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 1, 4], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 4, 1, 3], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]} "Class ", 4619, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], %1}, {[[1, 4, 2, 3], [1, 1, 1]], %2}, {[[2, 3, 1, 4], [1, 1, 1]], %2}, {%2, [[2, 4, 3, 1], [1, 1, 1]]}, {%2, [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], %1}, {%1, [[3, 2, 4, 1], [1, 1, 1]]}, {%1, [[4, 1, 3, 2], [1, 1, 1]]}} %1 := [[3, 1, 4, 2], [1, 1, 1]] %2 := [[2, 4, 1, 3], [1, 1, 1]] {[[1, 3, 4, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], %2}, {[[1, 4, 2, 3], [1, 1, 1]], %1}, {[[2, 3, 1, 4], [1, 1, 1]], %1}, {%1, [[2, 4, 3, 1], [1, 1, 1]]}, {%1, [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], %2}, {%2, [[3, 2, 4, 1], [1, 1, 1]]}, {%2, [[4, 1, 3, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 4, 2, 3], [1, 1, 1]], %1}, " has scheme:" %1 := [[2, 4, 1, 3], [1, 1, 1]] %2 := [[3, 1, 4, 2], [1, 1, 1]] {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174] "" "Class ", 4620, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[3, 2, 4, 1], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {[0, 1, 0, 1]}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 1, 0, 1]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {3}, {[0, 0, 1, 0, 1], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}], [[2, 1, 3, 4], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {[0, 0, 1, 0, 1], [0, 1, 0, 0, 1]}], [[2, 3, 1, 4], {1}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {}, {[0, 0, 1, 0, 1], [0, 1, 0, 0, 1]}], [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1]}], [[3, 1, 2, 4], {2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {[0, 1, 0, 0, 1], [0, 1, 0, 1, 0]}], [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 1], [0, 1, 0, 1, 0]}], [[3, 4, 2, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 1], [0, 1, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3, 5], {1, 2}, %1], [ [2, 1, 5, 3, 4], {4}, {[0, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0]}], [[2, 4, 1, 3, 5], {1, 3}, %1], [[2, 5, 1, 3, 4], {4}, {[0, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 5, 1, 4, 3], {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 1, 0]}], [[3, 1, 4, 2, 5], {1, 2}, %1], [[3, 1, 5, 2, 4], {2}, {[0, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [ [3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0]}], [ [3, 2, 5, 4, 1], {1, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [[3, 4, 1, 2, 5], {1, 3}, {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 5, 1, 2, 4], {3}, {[0, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 0]}], [ [3, 5, 1, 4, 2], {2}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0]}], [ [3, 5, 2, 4, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [ [4, 1, 5, 2, 3], {4}, {[0, 0, 1, 0, 0, 1], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [4, 1, 5, 3, 2], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0]}], [[4, 2, 5, 3, 1], {1, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [ [4, 5, 1, 2, 3], {3}, {[0, 0, 1, 0, 0, 1], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0]}], [ [4, 5, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]} %1 := {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 86, 336, 1290, 4870, 18164, 67234, 247786, 911120, 3346618, 12286942, 45104548, 165573482, 607817410, 2231360192, 8191763970, 30074097062] "" "Class ", 4621, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, %1], [[1, 4, 2, 3], {3}, %1], [[1, 4, 3, 2], {3}, {}], [[2, 1, 3, 4], {1, 2}, %1], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {3}, %1], [[2, 4, 3, 1], {3}, {}], [[3, 1, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[2, 1, 4, 3, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 1, 5, 3, 4], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 5, 4, 2], {1, 4}, {[0, 1, 0, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 4}, {}]} %1 := {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 88, 366, 1552, 6652, 28696, 124310, 540040, 2350820, 10248248, 44725516, 195354368, 853829272, 3733693872, 16333556838, 71476391800, 312865382004] "" "Class ", 4622, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], %1}, {[[1, 4, 2, 3], [1, 1, 1]], %1}, {%2, [[2, 4, 3, 1], [1, 1, 1]]}, {%2, [[3, 2, 4, 1], [1, 1, 1]]}, {%2, [[4, 1, 3, 2], [1, 1, 1]]}, {%2, [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], %1}, {[[3, 1, 2, 4], [1, 1, 1]], %1}} %1 := [[3, 4, 1, 2], [1, 1, 1]] %2 := [[2, 1, 4, 3], [1, 1, 1]] {[[1, 3, 4, 2], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[1, 4, 2, 3], [1, 1, 1]], [[3, 4, 1, 2], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[2, 4, 3, 1], [1, 1, 1]]} {[[2, 1, 4, 3], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]} "Class ", 4623, " is:" {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}} {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]} "For the class ", {{[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, {[[1, 4, 3, 2], [1, 1, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 2, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, {[[3, 2, 1, 4], [1, 1, 1]], [[4, 1, 3, 2], [1, 1, 1]]}}, " the pattern set ", {[[1, 3, 4, 2], [1, 1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {[0, 0, 1, 1, 0]}], [[2, 1, 3, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {1}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {3}, {[0, 0, 1, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1}, {}], [[3, 4, 1, 2], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[3, 4, 2, 1], {3}, {}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[4, 2, 3, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [2, 1, 5, 3, 4], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {4}, {[0, 0, 0, 1, 1, 0]}], [[3, 1, 4, 2, 5], {1, 2, 3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [ [3, 1, 5, 2, 4], {1, 2}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {4}, {[0, 0, 0, 1, 1, 0], [0, 0, 1, 0, 0, 0]}], [[3, 2, 5, 4, 1], {1, 4}, {[0, 0, 0, 1, 1, 0], [0, 0, 1, 0, 1, 0]}], [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}], [[4, 2, 5, 3, 1], {1, 4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 22, 87, 352, 1434, 5861, 24019, 98677, 406291, 1676009, 6924618, 28646875, 118638038, 491765865, 2039944740, 8467475533, 35166107745, 146115418937] "" "Class ", 4624, " is:" {{[[1, 4, 3, 2], [1, 1, 1]], %2}, {[[1, 4, 3, 2], [1, 1, 1]], %1}, {[[2, 3, 4, 1], [1, 1, 1]], %2}, {[[2, 3, 4, 1], [1, 1, 1]], %1}, {%2, [[3, 2, 1, 4], [1, 1, 1]]}, {%2, [[4, 1, 2, 3], [1, 1, 1]]}, {%1, [[3, 2, 1, 4], [1, 1, 1]]}, {%1, [[4, 1, 2, 3], [1, 1, 1]]}} %1 := [[3, 1, 4, 2], [1, 1, 1]] %2 := [[2, 4, 1, 3], [1, 1, 1]] {[[1, 4, 3, 2], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[1, 4, 3, 2], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[2, 4, 1, 3], [1, 1, 1]]} {[[2, 3, 4, 1], [1, 1, 1]], [[3, 1, 4, 2], [1, 1, 1]]} "Out of the ", 4624, " equivalence classes ", 1600, "(or ", 34.60207612, " %) classes have enumeration schemes." 3024, "(or ", 65.39792388, " %) classes do not have enumeration schemes of depth <=", 5, ", with gap vectors of weight <=", 2 "The classes that failed are: " {{{%180, %139}}, {{%180, %14}}, {{%180, %32}}, {{%180, %6}}, {{%180, %25}}, {{%180, %22}}, {{%180, %3}}, {{%180, %29}}, {{%180, %23}}, {{%180, %1}}, {{%180, %34}}, {{%180, %8}}, {{%180, %143}}, {{%180, %134}}, {{%180, [[4, 3, 2, 1], [0, 1, 0]]}}, {{%180, %173}}, {{%177, %172}}, {{%177, %144}}, {{%177, %139}}, {{%177, %133}}, {{%177, %14}}, {{%177, %41}}, {{%177, %37}}, {{%177, %32}}, {{%177, %6}}, {{%177, %30}}, {{%177, %25}}, {{%177, %22}}, {{%177, %3}}, {{%177, %45}}, {{%177, %29}}, {{%177, %23}}, {{%177, %1}}, {{%177, %44}}, {{%177, %42}}, {{%177, %34}}, {{%177, %8}}, {{%177, %149}}, {{%177, %143}}, {{%177, [[4, 2, 3, 1], [1, 0, 1]]}}, {{%177, %134}}, {{%177, [[4, 3, 2, 1], [0, 1, 0]]}}, {{%177, %173}}, {{%175, %174}}, {{%175, %176}}, {{%172, %139}}, {{%172, %14}}, {{%172, %32}}, {{%172, %6}}, {{%172, %25}}, {{%172, %22}}, {{%172, %3}}, {{%172, %29}}, {{%172, %23}}, {{%172, %1}}, {{%172, %42}}, {{%172, %34}}, {{%172, %8}}, {{%172, %143}}, {{%172, %134}}, {{%172, %173}}, {{%18, %139}}, {{%18, %41}}, {{%18, %37}}, {{%18, %32}}, {{%18, %30}}, {{%18, %25}}, {{%18, %22}}, {{%18, %45}}, {{%18, %29}}, {{%18, %23}}, {{%18, %44}}, {{%18, %42}}, {{%18, %34}}, {{%18, %8}}, {{%18, %149}}, {{%18, %143}}, {{%18, %134}}, {{%18, %173}}, {{%165, %166}}, {{%165, %164}}, {{%162, %161}}, {{%162, %163}}, {{%159, %160}}, {{%159, %157}}, {{%152, %153}}, {{%152, %150}}, {{%147, %146}}, 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{{%49, %27}, {%47, %28}}, {{%49, %25}, {%47, %29}}, {{%49, %20}, {%47, %21}}, {{%49, %26}, {%47, %31}}, {{%49, %22}, {%47, %23}}, {{%49, %19}, {%47, %24}}, {{%49, %3}, {%47, %1}}, {{%49, %45}, {%47, %30}}, {{%49, %31}, {%47, %26}}, {{%49, %29}, {%47, %25}}, {{%49, %24}, {%47, %19}}, {{%49, %28}, {%47, %27}}, {{%49, %23}, {%47, %22}}, {{%49, %21}, {%47, %20}}, {{%49, %1}, {%47, %3}}, {{%49, %46}, {%4, %50}}, {{%49, %44}, {%41, %47}}, {{%49, %43}, {%38, %47}}, {{%49, %42}, {%37, %47}}, {{%49, %40}, {%39, %47}}, {{%49, %34}, {%32, %47}}, {{%49, %33}, {%35, %47}}, {{%49, %8}, {%6, %47}}, {{%49, %51}, {%47, %50}}, {{%49, %48}, {%47, %46}}, {{%4, %41}, {%41, %46}}, {{%4, %39}, {%38, %46}}, {{%4, %37}, {%37, %46}}, {{%4, %38}, {%39, %46}}, {{%4, %32}, {%32, %46}}, {{%4, %36}, {%35, %46}}, {{%4, %6}, {%6, %46}}, {{%4, %30}, {%2, %45}}, {{%4, %27}, {%2, %28}}, {{%4, %25}, {%2, %29}}, {{%4, %26}, {%2, %31}}, {{%4, %22}, {%2, %23}}, {{%4, %19}, {%2, %24}}, {{%4, %45}, {%2, %30}}, {{%4, %31}, {%2, %26}}, {{%4, %29}, {%2, %25}}, {{%4, %24}, {%2, %19}}, {{%4, %28}, {%2, %27}}, {{%4, %23}, {%2, %22}}, {{%4, %21}, {%2, %20}}, {{%4, %44}, {%41, %2}}, {{%4, %43}, {%38, %2}}, {{%4, %42}, {%37, %2}}, {{%4, %40}, {%39, %2}}, {{%4, %34}, {%32, %2}}, {{%4, %33}, {%35, %2}}, {{%4, %8}, {%6, %2}}, {{%41, %20}, {%41, %19}}, {{%41, %24}, {%41, %21}}, {{%39, %37}, {%37, %38}}, {{%39, %36}, {%35, %38}}, {{%39, %25}, {%38, %25}}, {{%39, %20}, {%38, %19}}, {{%39, %26}, {%38, %27}}, {{%39, %22}, {%38, %22}}, {{%39, %19}, {%38, %20}}, {{%39, %3}, {%38, %3}}, {{%39, %29}, {%38, %29}}, {{%39, %24}, {%38, %21}}, {{%39, %28}, {%38, %31}}, {{%39, %23}, {%38, %23}}, {{%39, %21}, {%38, %24}}, {{%39, %1}, {%38, %1}}, {{%39, %34}, {%38, %34}}, {{%39, %33}, {%35, %40}}, {{%39, %8}, {%38, %8}}, {{%37, %20}, {%37, %19}}, {{%37, %31}, {%37, %28}}, {{%37, %24}, {%37, %21}}, {{%35, %32}, {%32, %36}}, {{%35, %25}, {%36, %25}}, {{%35, %20}, {%36, %19}}, {{%35, %26}, {%36, %27}}, {{%35, %22}, {%36, %22}}, {{%35, %19}, {%36, %20}}, {{%35, %3}, {%36, %3}}, {{%35, %29}, {%36, %29}}, {{%35, %24}, {%36, %21}}, {{%35, %28}, {%36, %31}}, {{%35, %23}, {%36, %23}}, {{%35, %21}, {%36, %24}}, {{%35, %1}, {%36, %1}}, {{%35, %34}, {%32, %33}}, {{%32, %27}, {%32, %26}}, {{%32, %20}, {%32, %19}}, {{%32, %31}, {%32, %28}}, {{%32, %24}, {%32, %21}}, {{%6, %27}, {%6, %26}}, {{%6, %20}, {%6, %19}}, {{%6, %3}, {%6, %1}}, {{%6, %31}, {%6, %28}}, {{%6, %24}, {%6, %21}}, {{%30, %24}, {%30, %21}}, {{%27, %25}, {%25, %26}}, {{%27, %19}, {%20, %26}}, {{%27, %29}, {%25, %28}}, {{%27, %24}, {%26, %21}}, {{%27, %23}, {%26, %23}}, {{%27, %21}, {%20, %28}}, {{%27, %1}, {%26, %1}}, {{%25, %24}, {%25, %21}}, {{%20, %22}, {%22, %19}}, {{%20, %24}, {%19, %21}}, {{%20, %23}, {%22, %21}}, {{%20, %1}, {%19, %1}}, {{%18, %7}, {%18, %5}, {%18, %15}, {%18, %13}}, {{%17, %3}, {%17, %1}, {%16, %3}, {%16, %1}}, {{%14, %7}, {%14, %5}, {%14, %15}, {%14, %13}}, {{%10, %3}, {%9, %1}, {%12, %1}, {%3, %11}}, {{%10, %8}, {%9, %8}, {%6, %7}, {%6, %5}}, {{%4, %3}, {%4, %1}, {%2, %3}, {%2, %1}}} %1 := [[3, 1, 4, 2], [1, 1, 1]] %2 := [[2, 3, 4, 1], [1, 1, 1]] %3 := [[2, 4, 1, 3], [1, 1, 1]] %4 := [[1, 4, 3, 2], [1, 1, 1]] %5 := [[3, 2, 4, 1], [1, 1, 1]] %6 := [[2, 1, 4, 3], [1, 1, 1]] %7 := [[2, 4, 3, 1], [1, 1, 1]] %8 := [[3, 4, 1, 2], [1, 1, 1]] %9 := [[1, 4, 2, 3], [1, 1, 1]] %10 := [[1, 3, 4, 2], [1, 1, 1]] %11 := [[3, 1, 2, 4], [1, 1, 1]] %12 := [[2, 3, 1, 4], [1, 1, 1]] %13 := [[4, 2, 1, 3], [1, 1, 1]] %14 := [[1, 3, 2, 4], [1, 1, 1]] %15 := [[4, 1, 3, 2], [1, 1, 1]] %16 := [[2, 1, 3, 4], [1, 1, 1]] %17 := [[1, 2, 4, 3], [1, 1, 1]] %18 := [[1, 2, 3, 4], [1, 1, 1]] %19 := [[2, 4, 1, 3], [1, 1, 0]] %20 := [[2, 4, 1, 3], [0, 1, 1]] %21 := [[3, 1, 4, 2], [1, 1, 0]] %22 := [[2, 4, 1, 3], [1, 0, 1]] %23 := [[3, 1, 4, 2], [1, 0, 1]] %24 := [[3, 1, 4, 2], [0, 1, 1]] %25 := [[2, 4, 1, 3], [0, 1, 0]] %26 := [[2, 4, 1, 3], [1, 0, 0]] %27 := [[2, 4, 1, 3], [0, 0, 1]] %28 := [[3, 1, 4, 2], [1, 0, 0]] %29 := [[3, 1, 4, 2], [0, 1, 0]] %30 := [[2, 4, 1, 3], [0, 0, 0]] %31 := [[3, 1, 4, 2], [0, 0, 1]] %32 := [[2, 1, 4, 3], [1, 0, 1]] %33 := [[3, 4, 1, 2], [1, 1, 0]] %34 := [[3, 4, 1, 2], [1, 0, 1]] %35 := [[2, 1, 4, 3], [0, 1, 1]] %36 := [[2, 1, 4, 3], [1, 1, 0]] %37 := [[2, 1, 4, 3], [0, 1, 0]] %38 := [[2, 1, 4, 3], [1, 0, 0]] %39 := [[2, 1, 4, 3], [0, 0, 1]] %40 := [[3, 4, 1, 2], [1, 0, 0]] %41 := [[2, 1, 4, 3], [0, 0, 0]] %42 := [[3, 4, 1, 2], [0, 1, 0]] %43 := [[3, 4, 1, 2], [0, 0, 1]] %44 := [[3, 4, 1, 2], [0, 0, 0]] %45 := [[3, 1, 4, 2], [0, 0, 0]] %46 := [[3, 2, 1, 4], [1, 1, 1]] %47 := [[2, 3, 4, 1], [0, 1, 1]] %48 := [[4, 1, 2, 3], [1, 1, 1]] %49 := [[1, 4, 3, 2], [1, 1, 0]] %50 := [[3, 2, 1, 4], [0, 1, 1]] %51 := [[4, 1, 2, 3], [1, 1, 0]] %52 := [[2, 3, 4, 1], [1, 0, 1]] %53 := [[1, 4, 3, 2], [1, 0, 1]] %54 := [[3, 2, 1, 4], [1, 0, 1]] %55 := [[2, 3, 4, 1], [0, 0, 1]] %56 := [[1, 4, 3, 2], [1, 0, 0]] %57 := [[3, 2, 1, 4], [0, 0, 1]] %58 := [[2, 3, 4, 1], [1, 1, 0]] %59 := [[1, 4, 3, 2], [0, 1, 1]] %60 := [[3, 2, 1, 4], [1, 1, 0]] %61 := [[4, 1, 2, 3], [1, 0, 1]] %62 := [[4, 1, 2, 3], [1, 0, 0]] %63 := [[4, 1, 2, 3], [0, 1, 1]] %64 := [[2, 3, 4, 1], [0, 1, 0]] %65 := [[1, 4, 3, 2], [0, 1, 0]] %66 := [[3, 2, 1, 4], [0, 1, 0]] %67 := [[4, 1, 2, 3], [0, 1, 0]] %68 := [[3, 4, 1, 2], [0, 1, 1]] %69 := [[2, 3, 4, 1], [1, 0, 0]] %70 := [[1, 4, 3, 2], [0, 0, 1]] %71 := [[3, 2, 1, 4], [1, 0, 0]] %72 := [[2, 3, 4, 1], [0, 0, 0]] %73 := [[1, 4, 3, 2], [0, 0, 0]] %74 := [[3, 2, 1, 4], [0, 0, 0]] %75 := [[4, 1, 2, 3], [0, 0, 1]] %76 := [[4, 1, 2, 3], [0, 0, 0]] %77 := [[2, 3, 1, 4], [0, 1, 1]] %78 := [[1, 4, 2, 3], [1, 1, 0]] %79 := [[3, 2, 4, 1], [0, 1, 1]] %80 := [[4, 1, 3, 2], [1, 1, 0]] %81 := [[2, 3, 1, 4], [1, 0, 1]] %82 := [[1, 4, 2, 3], [1, 0, 1]] %83 := [[3, 2, 4, 1], [1, 0, 1]] %84 := [[2, 3, 1, 4], [0, 0, 1]] %85 := [[1, 4, 2, 3], [1, 0, 0]] %86 := [[3, 2, 4, 1], [0, 0, 1]] %87 := [[2, 3, 1, 4], [1, 1, 0]] %88 := [[1, 4, 2, 3], [0, 1, 1]] %89 := [[3, 2, 4, 1], [1, 1, 0]] %90 := [[4, 1, 3, 2], [1, 0, 1]] %91 := [[4, 1, 3, 2], [1, 0, 0]] %92 := [[4, 1, 3, 2], [0, 1, 1]] %93 := [[2, 3, 1, 4], [0, 1, 0]] %94 := [[1, 4, 2, 3], [0, 1, 0]] %95 := [[3, 2, 4, 1], [0, 1, 0]] %96 := [[4, 1, 3, 2], [0, 1, 0]] %97 := [[2, 3, 1, 4], [1, 0, 0]] %98 := [[1, 4, 2, 3], [0, 0, 1]] %99 := [[3, 2, 4, 1], [1, 0, 0]] %100 := [[2, 3, 1, 4], [0, 0, 0]] %101 := [[1, 4, 2, 3], [0, 0, 0]] %102 := [[3, 2, 4, 1], [0, 0, 0]] %103 := [[4, 1, 3, 2], [0, 0, 1]] %104 := [[4, 1, 3, 2], [0, 0, 0]] %105 := [[2, 4, 3, 1], [0, 1, 1]] %106 := [[1, 3, 4, 2], [1, 1, 0]] %107 := [[3, 1, 2, 4], [0, 1, 1]] %108 := [[4, 2, 1, 3], [1, 1, 0]] %109 := [[3, 1, 2, 4], [1, 0, 1]] %110 := [[1, 3, 4, 2], [1, 0, 1]] %111 := [[2, 4, 3, 1], [1, 0, 1]] %112 := [[2, 4, 3, 1], [0, 0, 1]] %113 := [[1, 3, 4, 2], [1, 0, 0]] %114 := [[3, 1, 2, 4], [0, 0, 1]] %115 := [[2, 4, 3, 1], [1, 1, 0]] %116 := [[1, 3, 4, 2], [0, 1, 1]] %117 := [[3, 1, 2, 4], [1, 1, 0]] %118 := [[4, 2, 1, 3], [1, 0, 0]] %119 := [[4, 2, 1, 3], [0, 1, 1]] %120 := [[2, 4, 3, 1], [0, 1, 0]] %121 := [[1, 3, 4, 2], [0, 1, 0]] %122 := [[4, 2, 1, 3], [1, 0, 1]] %123 := [[3, 1, 2, 4], [0, 1, 0]] %124 := [[4, 2, 1, 3], [0, 1, 0]] %125 := [[2, 4, 3, 1], [1, 0, 0]] %126 := [[1, 3, 4, 2], [0, 0, 1]] %127 := [[3, 1, 2, 4], [1, 0, 0]] %128 := [[2, 4, 3, 1], [0, 0, 0]] %129 := [[1, 3, 4, 2], [0, 0, 0]] %130 := [[3, 1, 2, 4], [0, 0, 0]] %131 := [[4, 2, 1, 3], [0, 0, 1]] %132 := [[4, 2, 1, 3], [0, 0, 0]] %133 := [[1, 3, 2, 4], [1, 0, 1]] %134 := [[4, 2, 3, 1], [1, 1, 1]] %135 := [[1, 3, 2, 4], [1, 1, 0]] %136 := [[1, 3, 2, 4], [0, 1, 1]] %137 := [[4, 2, 3, 1], [1, 1, 0]] %138 := [[4, 2, 3, 1], [0, 1, 1]] %139 := [[1, 3, 2, 4], [0, 1, 0]] %140 := [[1, 3, 2, 4], [1, 0, 0]] %141 := [[1, 3, 2, 4], [0, 0, 1]] %142 := [[4, 2, 3, 1], [1, 0, 0]] %143 := [[4, 2, 3, 1], [0, 1, 0]] %144 := [[1, 3, 2, 4], [0, 0, 0]] %145 := [[3, 4, 2, 1], [1, 1, 1]] %146 := [[2, 1, 3, 4], [0, 1, 1]] %147 := [[1, 2, 4, 3], [1, 1, 0]] %148 := [[3, 4, 2, 1], [0, 1, 1]] %149 := [[4, 2, 3, 1], [0, 0, 0]] %150 := [[3, 4, 2, 1], [1, 0, 1]] %151 := [[4, 3, 1, 2], [1, 1, 0]] %152 := [[1, 2, 4, 3], [1, 0, 1]] %153 := [[2, 1, 3, 4], [1, 0, 1]] %154 := [[2, 1, 3, 4], [0, 0, 1]] %155 := [[1, 2, 4, 3], [1, 0, 0]] %156 := [[3, 4, 2, 1], [0, 0, 1]] %157 := [[3, 4, 2, 1], [1, 1, 0]] %158 := [[4, 3, 1, 2], [1, 0, 0]] %159 := [[1, 2, 4, 3], [0, 1, 1]] %160 := [[2, 1, 3, 4], [1, 1, 0]] %161 := [[2, 1, 3, 4], [0, 1, 0]] %162 := [[1, 2, 4, 3], [0, 1, 0]] %163 := [[3, 4, 2, 1], [0, 1, 0]] %164 := [[3, 4, 2, 1], [1, 0, 0]] %165 := [[1, 2, 4, 3], [0, 0, 1]] %166 := [[2, 1, 3, 4], [1, 0, 0]] %167 := [[3, 4, 2, 1], [0, 0, 0]] %168 := [[1, 2, 4, 3], [0, 0, 0]] %169 := [[2, 1, 3, 4], [0, 0, 0]] %170 := [[4, 3, 1, 2], [0, 1, 0]] %171 := [[4, 3, 1, 2], [0, 0, 0]] %172 := [[1, 2, 3, 4], [1, 0, 1]] %173 := [[4, 3, 2, 1], [1, 1, 1]] %174 := [[1, 2, 3, 4], [1, 1, 0]] %175 := [[1, 2, 3, 4], [0, 1, 1]] %176 := [[4, 3, 2, 1], [1, 1, 0]] %177 := [[1, 2, 3, 4], [0, 1, 0]] %178 := [[1, 2, 3, 4], [1, 0, 0]] %179 := [[1, 2, 3, 4], [0, 0, 1]] %180 := [[1, 2, 3, 4], [0, 0, 0]]