"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 ", 70, " equivalence classes of generalized patterns of lengths ", [3, 3] "Class ", 1, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 32, 122, 544, 2770, 15872, 101042, 707584, 5405530, 44736512, 398721962, 3807514624, 38783024290, 419730685952, 4809759350882, 58177770225664, 740742376475050] "" "Class ", 2, " is:" {{[[1, 2, 3], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[3, 2, 1], [1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1], [0, 2, 0]}], [[2, 1], {1}, {[0, 2, 0], [1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 3, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 1], [1, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {[1, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592, 75582] "" "Class ", 4, " is:" {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]]}, {[[3, 2, 1], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 2, 3], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 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, 5, 14, 43, 143, 509, 1922, 7651, 31965, 139685, 636712, 3020203, 14878176, 75982829, 401654560, 2194564531, 12377765239, 71980880885, 431114329728] "" "Class ", 5, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38] "" "Class ", 6, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1], [1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 7, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 11, 37, 149, 705, 3814, 23199, 156940, 1167862, 9478482, 83347221, 789272024, 8007691756, 86661018861, 996483990245, 12132147428205, 155914784843610, 2109180000370399] "" "Class ", 8, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 9, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 30, 108, 454, 2186, 11840, 71254, 471620, 3405444, 26638846, 224412432, 2025537526, 19501264282, 199486609542, 2160670133172, 24702689130878, 297287351106034] "" "Class ", 10, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]} "Class ", 11, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]} "Class ", 12, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 13, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 22, 58, 164, 496, 1601, 5502, 20075, 77531, 315947, 1354279, 6087421, 28611385, 140239297, 715116827, 3785445032, 20760746393] "" "Class ", 14, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 15, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 16, " is:" {{[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 17, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568504, 2390480, 10349536, 46206736, 211799312, 997313824, 4809701440, 23758664096] "" "Class ", 18, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 19, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568504, 2390480, 10349536, 46206736, 211799312, 997313824, 4809701440, 23758664096] "" "Class ", 20, " is:" {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[1, 3, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 21, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 11, 39, 161, 784, 4368, 27260, 189540, 1448860, 12076408, 109102564, 1061259548, 11060323280, 122963473024, 1452414435968, 18164949751872, 239807221886128, 3332441297971360] "" "Class ", 22, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 30, 104, 406, 1754, 8280, 42294, 231950, 1357140, 8427194, 55288874, 381798644, 2765917090, 20960284294, 165729739608, 1364153612318, 11665484410114] "" "Class ", 23, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 24, " is:" {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 25, " is:" {{[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 0]]}} {[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[1, 2, 3], [0, 1]], [[3, 2, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [0, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 0]], [[3, 2, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[1, 0, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 17, 43, 108, 321, 909, 3057, 9510, 35355, 118845, 480735, 1726200, 7510545, 28565145, 132517665, 530388810, 2605571955] "" "Class ", 26, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 27, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 28, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 29, " is:" {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[1, 3, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 30, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568504, 2390480, 10349536, 46206736, 211799312, 997313824, 4809701440, 23758664096] "" "Class ", 31, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568504, 2390480, 10349536, 46206736, 211799312, 997313824, 4809701440, 23758664096] "" "Class ", 32, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 33, " is:" {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]]} {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[1, 3, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 34, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 31, 108, 416, 1777, 8289, 41665, 224435, 1289186, 7853488, 50512489, 341824595, 2426151686, 18009930546, 139477305873, 1124437873839, 9417718833504] "" "Class ", 35, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 23, 65, 199, 654, 2296, 8569, 33825, 140581, 612933, 2795182, 13298464, 65852873, 338694479, 1805812309, 9963840219, 56807228074] "" "Class ", 36, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 37, " is:" {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}} {[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]]} {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 0]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [0, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 38, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 25, 83, 307, 1242, 5516, 26659, 138345, 765867, 4508137, 28090156, 184430578, 1271675747, 9183619179, 69280428647, 544652086415, 4452818599144 ] "" "Class ", 39, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191] "" "Class ", 40, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 41, " is:" {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191] "" "Class ", 42, " is:" {{[[1, 2, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1], [1, 0]]}} {[[1, 2, 3], [0, 1]], [[3, 2, 1], [1, 1]]} "For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 2, 1], [1, 0]]}}, " the pattern set ", {[[1, 2, 3], [0, 1]], [[3, 2, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {[1, 0, 0]}], [[2, 1, 3], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 5, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "" "Class ", 43, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 44, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 45, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019] "" "Class ", 46, " is:" {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[3, 1, 2], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[1, 3, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {1}, {[0, 2]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 47, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[1, 3, 2], [0, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 23, 63, 178, 514, 1515, 4545, 13827, 42540, 132124, 413741, 1304891, 4141198, 13214815, 42375461, 136478383, 441285890] "" "Class ", 48, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 49, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]]} {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191] "" "Class ", 50, " is:" {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}} {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", {{[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 2, 3], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 2, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 2, 1], [1, 1]]}}, " the pattern set ", {[[1, 2, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1], [1, 0, 0]}], [[2, 1], {1}, {[0, 1, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191] "" "Class ", 51, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 10, 29, 95, 350, 1426, 6343, 30552, 158177, 874646, 5138791, 31939208, 209199255, 1439200752, 10369053026, 78034862858, 612020248577, 4991933423569] "" "Class ", 52, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902, 253106837] "" "Class ", 53, " is:" {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902, 253106837] "" "Class ", 54, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[1, 0, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 55, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 56, " is:" {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]} {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 57, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, {[[1, 3, 2], [0, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 2], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902, 253106837] "" "Class ", 58, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 23, 66, 209, 718, 2645, 10373, 43090, 188803, 869191, 4189511, 21077302, 110389321, 600506833, 3386309222, 19759732535, 119118874709] "" "Class ", 59, " is:" {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}} {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]} "For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902, 253106837] "" "Class ", 60, " is:" {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[1, 3, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420] "" "Class ", 61, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 62, " is:" {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 63, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 64, " is:" {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]} {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2, 3}, {[0, 0, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 65, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, {[[1, 3, 2], [1, 0]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 0]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 2, 1], {2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 66, " is:" {{[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}} {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]} "For the class ", {{[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [0, 1]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 67, " is:" {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]} {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 3, 1], [1, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 1, 3], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {[0, 0, 1]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 68, " is:" {{[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}} {[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]} {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, {[[2, 1, 3], [0, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 0]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1], [0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 69, " is:" {{[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}} {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]} "For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [0, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 0]], [[3, 1, 2], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 1, 0]}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Class ", 70, " is:" {{[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}} {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]} "For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[1, 3, 2], [1, 1]], [[3, 1, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[2, 3, 1], [1, 1]]}, {[[2, 1, 3], [1, 1]], [[3, 1, 2], [1, 1]]}}, " the pattern set ", {[[1, 3, 2], [1, 1]], [[2, 3, 1], [1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0], [1, 0, 0]}], [[2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288] "" "Out of the ", 70, " equivalence classes ", 68, "(or ", 97.14285714, " %) classes have enumeration schemes." 2, "(or ", 2.857142857, " %) classes do not have enumeration schemes of depth <=", 5, ", with gap vectors of weight <=", 2 "The classes that failed are: " {{{[[1, 3, 2], [0, 1]], [[2, 1, 3], [1, 0]]}}, {{[[1, 3, 2], [0, 1]], [[2, 3, 1], [1, 0]]}}}