"There are ", 65, " pattern sets of type ", [4] "They fall into ", 21, " trivial pattern classes." "---------------------------------------------" "For the equivalence class ", {{[0, 0, 0, 0]}}, " the pattern set ", {[0, 0, 0, 0]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 3]}], [[1], {1}, {[[0, 0], 4]}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 208, 1520, 12840, 122640, 1303680, 15240960, 194140800] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 72, 16, 0] [120, 600, 600, 200, 0, 0] [720, 4320, 5400, 2400, 0, 0, 0] [5040, 35280, 52920, 29400, 0, 0, 0, 0] [40320, 322560, 564480, 376320, 0, 0, 0, 0, 0] [362880, 3265920, 6531840, 5080320, 0, 0, 0, 0, 0, 0] [3628800, 36288000, 81648000, 72576000, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 0, 0, 1]}, {[1, 0, 0, 0]}}, " the pattern set ", {[0, 0, 0, 1]}, " has the scheme ", [ [[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {}, {}], [[0, 1], {2}, {}], [[0, 0, 0], {1, 2, 3}, {[[1], 0]}], [[0, 0, 1], {3}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 205, 1456, 11839, 108214, 1097401, 12222460, 148289611] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 72, 12, 1] [120, 600, 600, 120, 15, 1] [720, 4320, 5400, 1200, 180, 18, 1] [5040, 35280, 52920, 12600, 2100, 252, 21, 1] [40320, 322560, 564480, 141120, 25200, 3360, 336, 24, 1] [362880, 3265920, 6531840, 1693440, 317520, 45360, 5040, 432, 27, 1] [3628800, 36288000, 81648000, 21772800, 4233600, 635040, 75600, 7200, 540, 30, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 0, 1, 0]}, {[0, 1, 0, 0]}}, " the pattern set ", {[0, 0, 1, 0]}, " has the scheme ", [ [[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {}, {}], [[0, 1], {2}, {}], [[0, 0, 0], {1}, {}], [[0, 0, 1], {1, 2, 3}, {[[0, 0], 1]}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 205, 1456, 11839, 108214, 1097401, 12222460, 148289611] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 72, 12, 1] [120, 600, 600, 120, 15, 1] [720, 4320, 5400, 1200, 180, 18, 1] [5040, 35280, 52920, 12600, 2100, 252, 21, 1] [40320, 322560, 564480, 141120, 25200, 3360, 336, 24, 1] [362880, 3265920, 6531840, 1693440, 317520, 45360, 5040, 432, 27, 1] [3628800, 36288000, 81648000, 21772800, 4233600, 635040, 75600, 7200, 540, 30, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1, 2, 0]}, {[0, 2, 1, 0]}}, " the pattern set ", {[0, 1, 2, 0]}, " has the scheme ", [ [[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {1}, {}], [[0, 1], {}, {}], [[0, 1, 0], {3}, {}], [[0, 1, 2], {1, 2, 3}, {[[0, 0, 0], 1]}], [[0, 2, 1], {2}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 203, 1406, 10992, 95628, 917499, 9641206, 110292968] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 66, 16, 1] [120, 600, 490, 170, 25, 1] [720, 4320, 3915, 1640, 360, 36, 1] [5040, 35280, 34251, 15995, 4340, 672, 49, 1] [40320, 322560, 328804, 164416, 50330, 9856, 1148, 64, 1] [362880, 3265920, 3452436, 1808436, 596106, 133434, 20076, 1836, 81, 1] [3628800, 36288000, 39456405, 21372240, 7398300, 1795752, 312900, 37680, 2790, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 0, 0, 2]}, {[2, 0, 0, 1]}}, " the pattern set ", {[1, 0, 0, 2]}, " has the scheme ", [ [[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {}, {}], [[1, 2], {2}, {}], [[2, 1], {1}, {}], [[1, 0, 0], {1, 2, 3}, {[[0, 1], 0]}], [[1, 0, 2], {3}, {}], [[2, 0, 1], {}, {}], [[2, 0, 1, 0], {1, 2}, {[[0, 0, 1], 0]}], [[2, 0, 1, 3], {4}, {}], [[3, 0, 1, 2], {4}, {}], [[3, 0, 2, 1], {3}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 203, 1406, 10977, 95089, 905137, 9404776, 106122929] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 66, 16, 1] [120, 600, 490, 170, 25, 1] [720, 4320, 3900, 1640, 360, 36, 1] [5040, 35280, 33852, 15855, 4340, 672, 49, 1] [40320, 322560, 321552, 159936, 49700, 9856, 1148, 64, 1] [362880, 3265920, 3336336, 1713936, 572292, 131418, 20076, 1836, 81, 1] [3628800, 36288000, 37666080, 19662720, 6822060, 1707048, 307650, 37680, 2790, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 2, 3, 4]}, {[4, 3, 2, 1]}}, " the pattern set ", {[1, 2, 3, 4]}, " has the scheme ", [ [[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {2}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 0], {3}, {}], [[1, 2, 3], {3}, {[[0, 0, 0, 1], 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 0], {4}, {}], [[2, 3, 1, 4], {4}, {[[0, 0, 0, 0, 1], 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 208, 1504, 12283, 109778, 1050820, 10614856, 111978128] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [23, 96, 72, 16, 1] [103, 575, 600, 200, 25, 1] [513, 3708, 5175, 2400, 450, 36, 1] [2761, 25137, 45423, 28175, 7350, 882, 49, 1] [15767, 176704, 402192, 323008, 112700, 18816, 1568, 64, 1] [94359, 1277127, 3578256, 3619728, 1635228, 365148, 42336, 2592, 81, 1] [586590, 9435900, 31928175, 39758400, 22623300, 6540912, 1014300, 86400, 4050, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 0, 1, 2]}, {[0, 0, 2, 1]}, {[1, 2, 0, 0]}, {[2, 1, 0, 0]}}, " the pattern set ", {[0, 0, 1, 2]}, " has the scheme ", [ [[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {}, {}], [[0, 1], {2}, {}], [[0, 0, 0], {1}, {}], [[0, 0, 1], {3}, {[[0, 1], 0]}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 203, 1406, 10992, 95628, 917499, 9641206, 110292968] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 66, 16, 1] [120, 600, 490, 170, 25, 1] [720, 4320, 3915, 1640, 360, 36, 1] [5040, 35280, 34251, 15995, 4340, 672, 49, 1] [40320, 322560, 328804, 164416, 50330, 9856, 1148, 64, 1] [362880, 3265920, 3452436, 1808436, 596106, 133434, 20076, 1836, 81, 1] [3628800, 36288000, 39456405, 21372240, 7398300, 1795752, 312900, 37680, 2790, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1, 0, 2]}, {[0, 2, 0, 1]}, {[1, 0, 2, 0]}, {[2, 0, 1, 0]}}, " the pattern set ", {[0, 1, 0, 2]}, " has the scheme ", [ [[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {1}, {}], [[0, 1], {}, {}], [[0, 1, 0], {2}, {[[0, 1], 0]}], [[0, 1, 2], {3}, {}], [[0, 2, 1], {2}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 203, 1406, 10977, 95124, 906467, 9436990, 106770293] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 66, 16, 1] [120, 600, 490, 170, 25, 1] [720, 4320, 3900, 1640, 360, 36, 1] [5040, 35280, 33852, 15890, 4340, 672, 49, 1] [40320, 322560, 321552, 161056, 49910, 9856, 1148, 64, 1] [362880, 3265920, 3336336, 1737456, 580230, 132174, 20076, 1836, 81, 1] [3628800, 36288000, 37666080, 20083200, 7013580, 1740312, 309750, 37680, 2790, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1, 2, 3]}, {[0, 3, 2, 1]}, {[1, 2, 3, 0]}, {[3, 2, 1, 0]}}, " the pattern set ", {[0, 1, 2, 3]}, " has the scheme ", [ [[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {1}, {}], [[0, 1], {}, {}], [[0, 1, 0], {3}, {}], [[0, 1, 2], {3}, {[[0, 0, 1], 0]}], [[0, 2, 1], {2}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 205, 1436, 11249, 96482, 895885, 8955292, 96120205] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 92, 72, 16, 1] [120, 530, 560, 200, 25, 1] [720, 3432, 4410, 2200, 450, 36, 1] [5040, 24948, 36162, 22750, 6650, 882, 49, 1] [40320, 203016, 315168, 231392, 87500, 16856, 1568, 64, 1] [362880, 1840014, 2960064, 2392992, 1083852, 275184, 37632, 2592, 81, 1] [3628800, 18448760, 30179790, 25783200, 13167000, 4085424, 746760, 76320, 4050, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1, 3, 2]}, {[0, 3, 1, 2]}, {[2, 1, 3, 0]}, {[2, 3, 1, 0]}}, " the pattern set ", {[0, 1, 3, 2]}, " has the scheme ", [ [[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {1}, {}], [[0, 1], {}, {}], [[0, 1, 0], {3}, {}], [[0, 1, 2], {2}, {[[0, 1, 0], 0]}], [[0, 2, 1], {2}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 205, 1436, 11249, 96482, 895885, 8955292, 96120205] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 92, 72, 16, 1] [120, 530, 560, 200, 25, 1] [720, 3432, 4410, 2200, 450, 36, 1] [5040, 24948, 36162, 22750, 6650, 882, 49, 1] [40320, 203016, 315168, 231392, 87500, 16856, 1568, 64, 1] [362880, 1840014, 2960064, 2392992, 1083852, 275184, 37632, 2592, 81, 1] [3628800, 18448760, 30179790, 25783200, 13167000, 4085424, 746760, 76320, 4050, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 0, 2, 3]}, {[1, 2, 0, 3]}, {[3, 0, 2, 1]}, {[3, 2, 0, 1]}}, " the pattern set ", {[1, 0, 2, 3]}, " has the scheme ", [ [[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {}, {}], [[1, 2], {2}, {}], [[2, 1], {1}, {}], [[1, 0, 0], {2}, {}], [[1, 0, 2], {3}, {[[0, 0, 1], 0]}], [[2, 0, 1], {}, {}], [[2, 0, 1, 0], {1, 2}, {}], [[2, 0, 1, 3], {4}, {[[0, 0, 0, 1], 0]}], [[3, 0, 1, 2], {4}, {}], [[3, 0, 2, 1], {3}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 205, 1436, 11243, 96202, 887853, 8770564, 92347585] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 92, 72, 16, 1] [120, 530, 560, 200, 25, 1] [720, 3426, 4410, 2200, 450, 36, 1] [5040, 24752, 36078, 22750, 6650, 882, 49, 1] [40320, 199016, 311696, 230832, 87500, 16856, 1568, 64, 1] [362880, 1772478, 2873952, 2364432, 1081332, 275184, 37632, 2592, 81, 1] [3628800, 17398070, 28468080, 24937200, 13011600, 4076604, 746760, 76320, 4050, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 0, 3, 2]}, {[2, 1, 0, 3]}, {[2, 3, 0, 1]}, {[3, 0, 1, 2]}}, " the pattern set ", {[1, 0, 3, 2]}, " has the scheme ", [ [[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {}, {}], [[1, 2], {2}, {}], [[2, 1], {1}, {}], [[1, 0, 0], {2}, {}], [[1, 0, 2], {3}, {[[0, 1, 0], 0]}], [[2, 0, 1], {}, {}], [[2, 0, 1, 0], {1, 2}, {}], [[2, 0, 1, 3], {4}, {[[0, 0, 1, 0], 0]}], [[3, 0, 1, 2], {4}, {}], [[3, 0, 2, 1], {3}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 205, 1436, 11243, 96202, 887853, 8770564, 92347585] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 92, 72, 16, 1] [120, 530, 560, 200, 25, 1] [720, 3426, 4410, 2200, 450, 36, 1] [5040, 24752, 36078, 22750, 6650, 882, 49, 1] [40320, 199016, 311696, 230832, 87500, 16856, 1568, 64, 1] [362880, 1772478, 2873952, 2364432, 1081332, 275184, 37632, 2592, 81, 1] [3628800, 17398070, 28468080, 24937200, 13011600, 4076604, 746760, 76320, 4050, 100, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 2, 4, 3]}, {[2, 1, 3, 4]}, {[3, 4, 2, 1]}, {[4, 3, 1, 2]}}, " the pattern set ", {[1, 2, 4, 3]}, " has the scheme ", [ [[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {2}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 0], {3}, {}], [[1, 2, 3], {2}, {[[0, 0, 1, 0], 0]}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 0], {4}, {}], [[2, 3, 1, 4], {1, 2}, {[[0, 0, 0, 1, 0], 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]] "First ", 10, " terms of the counting sequence are ", [2, 7, 34, 208, 1504, 12283, 109778, 1050820, 10614856, 111978128] "First ", 10, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 1] [23, 96, 72, 16, 1] [103, 575, 600, 200, 25, 1] [513, 3708, 5175, 2400, 450, 36, 1] [2761, 25137, 45423, 28175, 7350, 882, 49, 1] [15767, 176704, 402192, 323008, 112700, 18816, 1568, 64, 1] [94359, 1277127, 3578256, 3619728, 1635228, 365148, 42336, 2592, 81, 1] [586590, 9435900, 31928175, 39758400, 22623300, 6540912, 1014300, 86400, 4050, 100, 1] "---------------------------------------------" "Here are the failures: ", {{{[1, 3, 2, 4]}, {[4, 2, 3, 1]}}, {{[2, 1, 4, 3]}, {[3, 4, 1, 2]}}, {{[2, 4, 1, 3]}, {[3, 1, 4, 2]}}, {{[0, 2, 1, 3]}, {[0, 2, 3, 1]}, {[1, 3, 2, 0]}, {[3, 1, 2, 0]}}, {{[1, 3, 0, 2]}, {[2, 0, 1, 3]}, {[2, 0, 3, 1]}, {[3, 1, 0, 2]}}, {{[1, 3, 4, 2]}, {[2, 4, 3, 1]}, {[3, 1, 2, 4]}, {[4, 2, 1, 3]}}, {{[1, 4, 2, 3]}, {[2, 3, 1, 4]}, {[3, 2, 4, 1]}, {[4, 1, 3, 2]}}, {{[1, 4, 3, 2]}, {[2, 3, 4, 1]}, {[3, 2, 1, 4]}, {[4, 1, 2, 3]}}} "---------------------------------------------" "Overall, we found schemes for ", 13, " out of ", 21, " trivial classes, for a success rate of ", 0.6190476190