"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 ", 55, " equivalence classes of generalized patterns of lengths ", [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]]} "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]]}, " 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 111, 642, 4326, 33333, 288901, 2782082, 29471046, 340568843, 4263603891, 57482264322, 830335952166, 12793889924553, 209449977967081, 3630626729775362, 66429958806679686, 1279448352687538463] "" "Class ", 2, " is:" {{[[1, 2, 3, 4], [0, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 0]]}} {[[1, 2, 3, 4], [0, 1, 0]]} "For the class ", {{[[1, 2, 3, 4], [0, 1, 0]]}, {[[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4], [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], {3}, {}], [[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, 23, 107, 585, 3669, 25932, 203768, 1761109, 16595757, 169287873, 1857903529, 21823488238, 273130320026, 3627845694283, 50962676849199, 754814462534449, 11754778469338581, 191998054346198680] "" "Class ", 3, " is:" {{[[1, 2, 3, 4], [1, 0, 1]]}, {[[4, 3, 2, 1], [1, 0, 1]]}} {[[1, 2, 3, 4], [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]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2, 3}, {[0, 0, 0, 1]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 549, 3207, 20577, 143239, 1071704, 8555388, 72442465, 647479819, 6083742438, 59885558106, 615718710929, 6595077685263, 73424063891526, 847916751131054, 10138485386085013] "" "Class ", 4, " is:" {{[[1, 2, 3, 4], [1, 1, 1]]}, {[[4, 3, 2, 1], [1, 1, 1]]}} {[[1, 2, 3, 4], [1, 1, 1]]} "For the class ", {{[[1, 2, 3, 4], [1, 1, 1]]}, {[[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ", {[[1, 2, 3, 4], [1, 1, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {3}, {[0, 0, 0, 1]}], [[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, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089] "" "Class ", 5, " is:" {{[[1, 3, 2, 4], [0, 0, 0]]}, {[[4, 2, 3, 1], [0, 0, 0]]}} {[[1, 3, 2, 4], [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]]}, " 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 110, 632, 4229, 32337, 278204, 2659223, 27959880, 320706444, 3985116699, 53328433923, 764610089967, 11693644958690, 190015358010114, 3269272324528547, 59373764638615449, 1135048629795612125] "" "Class ", 6, " is:" {{[[1, 3, 2, 4], [0, 1, 0]]}, {[[4, 2, 3, 1], [0, 1, 0]]}} {[[1, 3, 2, 4], [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]]} "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]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[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, 23, 105, 549, 3207, 20577, 143239, 1071704, 8555388, 72442465, 647479819, 6083742438, 59885558106, 615718710929, 6595077685263, 73424063891526, 847916751131054, 10138485386085013] "" "Class ", 8, " is:" {{[[1, 3, 2, 4], [1, 1, 1]]}, {[[4, 2, 3, 1], [1, 1, 1]]}} {[[1, 3, 2, 4], [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]]} "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]]}, " 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, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 110, 631, 4223, 32301, 277962, 2657797, 27954521, 320752991, 3987045780, 53372351265, 765499019221, 11711207065229, 190365226548070, 3276401870322033, 59523410471007913, 1138295039078030599] "" "Class ", 10, " is:" {{[[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]]}} {[[2, 1, 4, 3], [0, 1, 0]]} "For the class ", {{[[2, 1, 4, 3], [0, 1, 0]]}, {[[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {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, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 585, 3669, 25932, 203768, 1761109, 16595757, 169287873, 1857903529, 21823488238, 273130320026, 3627845694283, 50962676849199, 754814462534449, 11754778469338581, 191998054346198680] "" "Class ", 11, " is:" {{[[2, 1, 4, 3], [1, 0, 1]]}, {[[3, 4, 1, 2], [1, 0, 1]]}} {[[2, 1, 4, 3], [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]]} "Class ", 13, " is:" {{[[2, 4, 1, 3], [0, 0, 0]]}, {[[3, 1, 4, 2], [0, 0, 0]]}} {[[2, 4, 1, 3], [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]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {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, 23, 110, 632, 4237, 32465, 279828, 2679950, 28232972, 324470844, 4039771856, 54165468774, 778128659247, 11923645252411, 194131328012012, 3346615262190736, 60897160676005110, 1166446154857250412] "" "Class ", 14, " is:" {{[[2, 4, 1, 3], [0, 1, 0]]}, {[[3, 1, 4, 2], [0, 1, 0]]}} {[[2, 4, 1, 3], [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]]} "Class ", 16, " is:" {{[[2, 4, 1, 3], [1, 1, 1]]}, {[[3, 1, 4, 2], [1, 1, 1]]}} {[[2, 4, 1, 3], [1, 1, 1]]} "Class ", 17, " 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]]} "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]]}, " 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 108, 598, 3815, 27532, 221708, 1970251, 19150132, 202064380, 2300071071, 28092017668, 366425723926, 5083645400819, 74745472084176, 1160974832572274, 18995175706664735, 326531476287842760] "" "Class ", 18, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[1, 2, 3, 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, 3, 2, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3, 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 550, 3228, 20878, 146994, 1116000, 9068288, 78384726, 717102126, 6913783826, 69991576572, 741642201619, 8202723500977, 94465859342678, 1130318929530706, 14024640055306543] "" "Class ", 19, " 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]]} "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]]}, " 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 110, 630, 4204, 32054, 274914, 2619692, 27459344, 313990182, 3889585408, 51888955808, 741668212080, 11307669002720, 183174676857608, 3141820432768752, 56882461258572976, 1084056190235653304] "" "Class ", 20, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[1, 2, 4, 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 584, 3660, 25910, 204564, 1782520, 16995202, 176008542, 1967664910, 23618071616, 302957562470, 4135988829879, 59876883929351, 916254180307702, 14777139719980648, 250523028439924015] "" "Class ", 21, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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], {3}, {}], [[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, 23, 107, 585, 3669, 25932, 203768, 1761109, 16595757, 169287873, 1857903529, 21823488238, 273130320026, 3627845694283, 50962676849199, 754814462534449, 11754778469338581, 191998054346198680] "" "Class ", 22, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[1, 2, 4, 3], [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, 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, 23, 105, 550, 3228, 20878, 146994, 1116000, 9068288, 78384726, 717102126, 6913783826, 69991576572, 741642201619, 8202723500977, 94465859342678, 1130318929530706, 14024640055306543] "" "Class ", 23, " 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]]} "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]]}, " 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], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 585, 3671, 25986, 204738, 1776327, 16824237, 172701135, 1909624371, 22626612450, 285982186662, 3840440707485, 54603776221965, 819424594880559, 12942757989763101, 214626518776190178] "" "Class ", 24, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 104, 532, 3004, 18426, 121393, 851810, 6325151, 49448313, 405298482, 3470885747, 30965656442, 287083987270, 2759838731485, 27458514900626, 282264050120512, 2993392570828096] "" "Class ", 25, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[1, 2, 4, 3], [1, 1, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[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}, {}], [[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}, {}], [[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, 105, 550, 3228, 20878, 146994, 1116000, 9068288, 78384726, 717102126, 6913783826, 69991576572, 741642201619, 8202723500977, 94465859342678, 1130318929530706, 14024640055306543] "" "Class ", 26, " 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]]} "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]]}, " 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], {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, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089] "" "Class ", 27, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[1, 3, 2, 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 585, 3671, 25986, 204738, 1776327, 16824237, 172701135, 1909624371, 22626612450, 285982186662, 3840440707485, 54603776221965, 819424594880559, 12942757989763101, 214626518776190178] "" "Class ", 28, " 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 ", 29, " 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]]} "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]]}, " 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 110, 630, 4210, 32150, 276210, 2636720, 27687440, 317169270, 3936056080, 52603684760, 753241509900, 11504852242400, 186705357825800, 3208160592252000, 58188413286031600, 1110946958902609400] "" "Class ", 30, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 584, 3660, 25910, 204564, 1782520, 16995202, 176008542, 1967664910, 23618071616, 302957562470, 4135988829879, 59876883929351, 916254180307702, 14777139719980648, 250523028439924015] "" "Class ", 31, " 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 ", 32, " 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 ", 33, " 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]]} "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]]}, " 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 585, 3671, 25986, 204738, 1776327, 16824237, 172701135, 1909624371, 22626612450, 285982186662, 3840440707485, 54603776221965, 819424594880559, 12942757989763101, 214626518776190178] "" "Class ", 34, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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}, {}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 549, 3207, 20577, 143239, 1071704, 8555388, 72442465, 647479819, 6083742438, 59885558106, 615718710929, 6595077685263, 73424063891526, 847916751131054, 10138485386085013] "" "Class ", 35, " 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 ", 36, " 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]]} "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]]}, " 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}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 110, 631, 4218, 32221, 276896, 2643883, 27768955, 318174363, 3949415431, 52794067318, 756137263377, 11551672922816, 187507250145806, 3222662529113641, 58464560588277289, 1116469710152742025] "" "Class ", 37, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[1, 4, 2, 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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 585, 3671, 25986, 204738, 1776327, 16824237, 172701135, 1909624371, 22626612450, 285982186662, 3840440707485, 54603776221965, 819424594880559, 12942757989763101, 214626518776190178] "" "Class ", 38, " 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 ", 39, " 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 ", 40, " 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]]} "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]]}, " 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], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 585, 3671, 25986, 204738, 1776327, 16824237, 172701135, 1909624371, 22626612450, 285982186662, 3840440707485, 54603776221965, 819424594880559, 12942757989763101, 214626518776190178] "" "Class ", 41, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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, 1, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 104, 532, 3004, 18426, 121393, 851810, 6325151, 49448313, 405298482, 3470885747, 30965656442, 287083987270, 2759838731485, 27458514900626, 282264050120512, 2993392570828096] "" "Class ", 42, " 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 ", 43, " 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]]} "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]]}, " 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}, {}], [[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, 23, 110, 630, 4210, 32150, 276210, 2636720, 27687440, 317169270, 3936056080, 52603684760, 753241509900, 11504852242400, 186705357825800, 3208160592252000, 58188413286031600, 1110946958902609400] "" "Class ", 44, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 582, 3622, 25369, 197523, 1692535, 15829557, 160463512, 1752529064, 20516018396, 256273980368, 3402364791737, 47841014687039, 710242228143271, 11101522062378069, 182234745428876525] "" "Class ", 45, " 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 ", 46, " 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 ", 47, " 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]]} "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]]}, " 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], {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, 23, 108, 598, 3815, 27532, 221708, 1970251, 19150132, 202064380, 2300071071, 28092017668, 366425723926, 5083645400819, 74745472084176, 1160974832572274, 18995175706664735, 326531476287842760] "" "Class ", 48, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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, 1, 0, 0]}], [[2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 105, 549, 3207, 20577, 143239, 1071704, 8555388, 72442465, 647479819, 6083742438, 59885558106, 615718710929, 6595077685263, 73424063891526, 847916751131054, 10138485386085013] "" "Class ", 49, " 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 ", 50, " is:" {{[[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [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]]} "Class ", 51, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[2, 1, 4, 3], [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}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 583, 3637, 25548, 199506, 1714383, 16075861, 163346039, 1787800653, 20968763454, 262377046698, 3488754384563, 49124073846495, 730212950439657, 11426842011345475, 187772980364922744] "" "Class ", 52, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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], {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, 23, 105, 550, 3228, 20878, 146994, 1116000, 9068288, 78384726, 717102126, 6913783826, 69991576572, 741642201619, 8202723500977, 94465859342678, 1130318929530706, 14024640055306543] "" "Class ", 53, " 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]]} "For the class ", {{[[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]]}}, " the pattern set ", {[[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], {1, 2}, {[0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 23, 107, 585, 3671, 25986, 204738, 1776327, 16824237, 172701135, 1909624371, 22626612450, 285982186662, 3840440707485, 54603776221965, 819424594880559, 12942757989763101, 214626518776190178] "" "Class ", 54, " 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 ", 55, " is:" {{[[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]]}, {[[3, 1, 2, 4], [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]]} {[[2, 4, 3, 1], [1, 1, 1]]} "Out of the ", 55, " equivalence classes ", 35, "(or ", 63.63636364, " %) classes have enumeration schemes." 20, "(or ", 36.36363636, " %) classes do not have enumeration schemes of depth <=", 5, ", with gap vectors of weight <=", 2 "The classes that failed are: " {{{[[1, 3, 2, 4], [0, 1, 0]]}}, {{[[1, 3, 2, 4], [1, 1, 1]]}}, {{[[2, 1, 4, 3], [1, 0, 1]]}}, {{[[2, 1, 4, 3], [1, 1, 1]]}}, {{[[2, 4, 1, 3], [0, 1, 0]]}}, {{[[2, 4, 1, 3], [1, 0, 1]]}}, {{[[2, 4, 1, 3], [1, 1, 1]]}}, {{[[1, 3, 2, 4], [0, 1, 1]]}, {[[1, 3, 2, 4], [1, 1, 0]]}}, {{[[1, 3, 4, 2], [0, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 0]]}}, {{[[1, 3, 4, 2], [0, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 0]]}}, {{[[1, 3, 4, 2], [1, 1, 0]]}, {[[2, 4, 3, 1], [0, 1, 1]]}}, {{[[1, 4, 2, 3], [0, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 0]]}}, {{[[1, 4, 2, 3], [0, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 0]]}}, {{[[1, 4, 2, 3], [1, 1, 0]]}, {[[2, 3, 1, 4], [0, 1, 1]]}}, {{[[1, 4, 3, 2], [0, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 0]]}}, {{[[1, 4, 3, 2], [0, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 0]]}}, {{[[1, 4, 3, 2], [1, 1, 0]]}, {[[2, 3, 4, 1], [0, 1, 1]]}}, {{[[1, 4, 3, 2], [1, 1, 1]]}, {[[2, 3, 4, 1], [1, 1, 1]]}}, {{[[2, 4, 1, 3], [0, 1, 1]]}, {[[2, 4, 1, 3], [1, 1, 0]]}}, { {[[1, 3, 4, 2], [1, 1, 1]]}, {[[1, 4, 2, 3], [1, 1, 1]]}, {[[2, 3, 1, 4], [1, 1, 1]]}, {[[2, 4, 3, 1], [1, 1, 1]]}}}