"There are ", 48, " pattern sets of type ", [2, 3] "They fall into ", 16, " trivial pattern classes." "---------------------------------------------" "For the equivalence class ", {{[0, 0], [1, 0, 2]}, {[0, 0], [2, 0, 1]}}, " the pattern set ", {[0, 0], [1, 0, 2]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 1]}], [[1], {}, {}], [[1, 0], {1, 2}, {[[0, 0], 1], [[0, 1], 0]}], [[1, 2], {2}, {[[0, 0, 0], 2]}], [[2, 1], {1}, {[[0, 0, 0], 2]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 21, 88, 440, 2592, 17724, 138624, 1223424, 12038400, 130711680, 1552296960, 20011829760, 278272834560, 4150929888000] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 0] [6, 15, 0, 0] [24, 64, 0, 0, 0] [120, 320, 0, 0, 0, 0] [720, 1872, 0, 0, 0, 0, 0] [5040, 12684, 0, 0, 0, 0, 0, 0] [40320, 98304, 0, 0, 0, 0, 0, 0, 0] [362880, 860544, 0, 0, 0, 0, 0, 0, 0, 0] [3628800, 8409600, 0, 0, 0, 0, 0, 0, 0, 0, 0] [39916800, 90794880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [479001600, 1073295360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [6227020800, 13784808960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [87178291200, 191094543360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1307674368000, 2843255520000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 0], [1, 2, 3]}, {[0, 0], [3, 2, 1]}}, " the pattern set ", {[0, 0], [1, 2, 3]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 1]}], [[1], {}, {}], [[1, 0], {2}, {[[0, 0], 1]}], [[1, 2], {2}, {[[0, 0, 0], 2], [[0, 0, 1], 0]}], [[2, 1], {1}, {[[0, 0, 0], 2]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 23, 94, 392, 1644, 6897, 28886, 120692, 502996, 2091102, 8673196, 35896928, 148282840, 611443845] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 0] [5, 18, 0, 0] [14, 80, 0, 0, 0] [42, 350, 0, 0, 0, 0] [132, 1512, 0, 0, 0, 0, 0] [429, 6468, 0, 0, 0, 0, 0, 0] [1430, 27456, 0, 0, 0, 0, 0, 0, 0] [4862, 115830, 0, 0, 0, 0, 0, 0, 0, 0] [16796, 486200, 0, 0, 0, 0, 0, 0, 0, 0, 0] [58786, 2032316, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [208012, 8465184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [742900, 35154028, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [2674440, 145608400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [9694845, 601749000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 1], [0, 0, 0]}, {[1, 0], [0, 0, 0]}}, " the pattern set ", {[0, 1], [0, 0, 0]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 2], [[1], 0]}], [[1], {1}, {[[0, 0], 3]}]] "First ", 15, " terms of the counting sequence are ", [2, 5, 15, 60, 300, 1800, 12600, 100800, 907200, 9072000, 99792000, 1197504000, 15567552000, 217945728000, 3269185920000] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 2, 1] [6, 6, 3, 0] [24, 24, 12, 0, 0] [120, 120, 60, 0, 0, 0] [720, 720, 360, 0, 0, 0, 0] [5040, 5040, 2520, 0, 0, 0, 0, 0] [40320, 40320, 20160, 0, 0, 0, 0, 0, 0] [362880, 362880, 181440, 0, 0, 0, 0, 0, 0, 0] [3628800, 3628800, 1814400, 0, 0, 0, 0, 0, 0, 0, 0] [39916800, 39916800, 19958400, 0, 0, 0, 0, 0, 0, 0, 0, 0] [479001600, 479001600, 239500800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [6227020800, 6227020800, 3113510400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [87178291200, 87178291200, 43589145600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1307674368000, 1307674368000, 653837184000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 1], [1, 0, 0]}, {[1, 0], [0, 0, 1]}}, " the pattern set ", {[0, 1], [1, 0, 0]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[1], 0]}], [[1], {1}, {[[0, 0], 2]}]] "First ", 15, " terms of the counting sequence are ", [2, 5, 13, 49, 241, 1441, 10081, 80641, 725761, 7257601, 79833601, 958003201, 12454041601, 174356582401, 2615348736001] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 2, 1] [6, 6, 0, 1] [24, 24, 0, 0, 1] [120, 120, 0, 0, 0, 1] [720, 720, 0, 0, 0, 0, 1] [5040, 5040, 0, 0, 0, 0, 0, 1] [40320, 40320, 0, 0, 0, 0, 0, 0, 1] [362880, 362880, 0, 0, 0, 0, 0, 0, 0, 1] [3628800, 3628800, 0, 0, 0, 0, 0, 0, 0, 0, 1] [39916800, 39916800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [479001600, 479001600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [6227020800, 6227020800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [87178291200, 87178291200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [1307674368000, 1307674368000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 2], [0, 0, 0]}, {[2, 1], [0, 0, 0]}}, " the pattern set ", {[1, 2], [0, 0, 0]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 2]}], [[1], {1}, {[[0, 0], 3], [[0, 1], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 19, 53, 126, 262, 491, 849, 1378, 2126, 3147, 4501, 6254, 8478, 11251] "First ", 15, " rows of the 0s triangle are: " [1, 1] [1, 4, 1] [1, 9, 9, 0] [1, 16, 36, 0, 0] [1, 25, 100, 0, 0, 0] [1, 36, 225, 0, 0, 0, 0] [1, 49, 441, 0, 0, 0, 0, 0] [1, 64, 784, 0, 0, 0, 0, 0, 0] [1, 81, 1296, 0, 0, 0, 0, 0, 0, 0] [1, 100, 2025, 0, 0, 0, 0, 0, 0, 0, 0] [1, 121, 3025, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 144, 4356, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 169, 6084, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 196, 8281, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 225, 11025, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[1, 2], [0, 1, 0]}, {[2, 1], [0, 1, 0]}}, " the pattern set ", {[1, 2], [0, 1, 0]}, " has the scheme ", [[[], {}, {}], [[0], {}, {}], [[1], {1}, {[[0, 1], 0]}], [[0, 0], {1}, {}], [[0, 1], {1, 2}, {[[0, 0], 1], [[0, 1], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 17, 44, 107, 250, 569, 1272, 2807, 6134, 13301, 28660, 61427, 131058, 278513] "First ", 15, " rows of the 0s triangle are: " [1, 1] [1, 4, 1] [1, 9, 6, 1] [1, 16, 18, 8, 1] [1, 25, 40, 30, 10, 1] [1, 36, 75, 80, 45, 12, 1] [1, 49, 126, 175, 140, 63, 14, 1] [1, 64, 196, 336, 350, 224, 84, 16, 1] [1, 81, 288, 588, 756, 630, 336, 108, 18, 1] [1, 100, 405, 960, 1470, 1512, 1050, 480, 135, 20, 1] [1, 121, 550, 1485, 2640, 3234, 2772, 1650, 660, 165, 22, 1] [1, 144, 726, 2200, 4455, 6336, 6468, 4752, 2475, 880, 198, 24, 1] [1, 169, 936, 3146, 7150, 11583, 13728, 12012, 7722, 3575, 1144, 234, 26, 1] [1, 196, 1183, 4368, 11011, 20020, 27027, 27456, 21021, 12012, 5005, 1456, 273, 28, 1] [1, 225, 1470, 5915, 16380, 33033, 50050, 57915, 51480, 35035, 18018, 6825, 1820, 315, 30, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 2], [2, 0, 1]}, {[2, 1], [1, 0, 2]}}, " the pattern set ", {[1, 2], [2, 0, 1]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {1, 2}, {[[0, 1], 0], [[1, 0], 0]}], [[1, 2], {1, 2}, {[[0, 0, 0], 0]}], [[2, 1], {1}, {[[0, 0, 1], 0], [[0, 1, 0], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 17, 44, 107, 250, 569, 1272, 2807, 6134, 13301, 28660, 61427, 131058, 278513] "First ", 15, " rows of the 0s triangle are: " [1, 1] [1, 4, 1] [1, 6, 9, 1] [1, 8, 18, 16, 1] [1, 10, 30, 40, 25, 1] [1, 12, 45, 80, 75, 36, 1] [1, 14, 63, 140, 175, 126, 49, 1] [1, 16, 84, 224, 350, 336, 196, 64, 1] [1, 18, 108, 336, 630, 756, 588, 288, 81, 1] [1, 20, 135, 480, 1050, 1512, 1470, 960, 405, 100, 1] [1, 22, 165, 660, 1650, 2772, 3234, 2640, 1485, 550, 121, 1] [1, 24, 198, 880, 2475, 4752, 6468, 6336, 4455, 2200, 726, 144, 1] [1, 26, 234, 1144, 3575, 7722, 12012, 13728, 11583, 7150, 3146, 936, 169, 1] [1, 28, 273, 1456, 5005, 12012, 21021, 27456, 27027, 20020, 11011, 4368, 1183, 196, 1] [1, 30, 315, 1820, 6825, 18018, 35035, 51480, 57915, 50050, 33033, 16380, 5915, 1470, 225, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 2], [3, 2, 1]}, {[2, 1], [1, 2, 3]}}, " the pattern set ", {[1, 2], [3, 2, 1]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[3], 0]}], [[1], {1}, {[[0, 1], 0], [[2, 0], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 19, 53, 126, 262, 491, 849, 1378, 2126, 3147, 4501, 6254, 8478, 11251] "First ", 15, " rows of the 0s triangle are: " [1, 1] [1, 4, 1] [0, 9, 9, 1] [0, 0, 36, 16, 1] [0, 0, 0, 100, 25, 1] [0, 0, 0, 0, 225, 36, 1] [0, 0, 0, 0, 0, 441, 49, 1] [0, 0, 0, 0, 0, 0, 784, 64, 1] [0, 0, 0, 0, 0, 0, 0, 1296, 81, 1] [0, 0, 0, 0, 0, 0, 0, 0, 2025, 100, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 3025, 121, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4356, 144, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6084, 169, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8281, 196, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11025, 225, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 0], [0, 1, 2]}, {[0, 0], [0, 2, 1]}, {[0, 0], [1, 2, 0]}, {[0, 0], [2, 1, 0]}}, " the pattern set ", {[0, 0], [0, 1, 2]}, " has the scheme ", [[[], {}, {}], [[0], {}, {}], [[1], {1}, {[[0, 0], 2]}], [[0, 0], {1, 2}, {[[0], 0]}], [[0, 1], {2}, {[[0, 0], 1], [[0, 1], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 21, 88, 445, 2676, 18739, 149920, 1349289, 13492900, 148421911, 1781062944, 23153818285, 324153456004, 4862301840075] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 0] [6, 15, 0, 0] [24, 64, 0, 0, 0] [120, 325, 0, 0, 0, 0] [720, 1956, 0, 0, 0, 0, 0] [5040, 13699, 0, 0, 0, 0, 0, 0] [40320, 109600, 0, 0, 0, 0, 0, 0, 0] [362880, 986409, 0, 0, 0, 0, 0, 0, 0, 0] [3628800, 9864100, 0, 0, 0, 0, 0, 0, 0, 0, 0] [39916800, 108505111, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [479001600, 1302061344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [6227020800, 16926797485, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [87178291200, 236975164804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1307674368000, 3554627472075, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 0], [1, 3, 2]}, {[0, 0], [2, 1, 3]}, {[0, 0], [2, 3, 1]}, {[0, 0], [3, 1, 2]}}, " the pattern set ", {[0, 0], [1, 3, 2]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 1]}], [[1], {}, {}], [[1, 0], {2}, {[[0, 0], 1]}], [[1, 2], {1}, {[[0, 0, 0], 2], [[0, 1, 0], 0]}], [[2, 1], {1}, {[[0, 0, 0], 2]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 23, 94, 392, 1644, 6897, 28886, 120692, 502996, 2091102, 8673196, 35896928, 148282840, 611443845] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 0] [5, 18, 0, 0] [14, 80, 0, 0, 0] [42, 350, 0, 0, 0, 0] [132, 1512, 0, 0, 0, 0, 0] [429, 6468, 0, 0, 0, 0, 0, 0] [1430, 27456, 0, 0, 0, 0, 0, 0, 0] [4862, 115830, 0, 0, 0, 0, 0, 0, 0, 0] [16796, 486200, 0, 0, 0, 0, 0, 0, 0, 0, 0] [58786, 2032316, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [208012, 8465184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [742900, 35154028, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [2674440, 145608400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [9694845, 601749000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 1], [1, 2, 0]}, {[0, 1], [2, 1, 0]}, {[1, 0], [0, 1, 2]}, {[1, 0], [0, 2, 1]}}, " the pattern set ", {[0, 1], [1, 2, 0]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[1], 0]}], [[1], {1}, {[[0, 1], 1]}]] "First ", 15, " terms of the counting sequence are ", [2, 5, 13, 39, 151, 783, 5167, 40575, 363391, 3629823, 39918847, 479005695, 6227028991, 87178307583, 1307674400767] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 2, 1] [6, 3, 3, 1] [24, 4, 6, 4, 1] [120, 5, 10, 10, 5, 1] [720, 6, 15, 20, 15, 6, 1] [5040, 7, 21, 35, 35, 21, 7, 1] [40320, 8, 28, 56, 70, 56, 28, 8, 1] [362880, 9, 36, 84, 126, 126, 84, 36, 9, 1] [3628800, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1] [39916800, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1] [479001600, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1] [6227020800, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1] [87178291200, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1] [1307674368000, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1], [1, 2, 3]}, {[0, 1], [3, 2, 1]}, {[1, 0], [1, 2, 3]}, {[1, 0], [3, 2, 1]}}, " the pattern set ", {[0, 1], [1, 2, 3]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[1], 0]}], [[1], {}, {}], [[1, 0], {1, 2}, {[[0, 1], 0], [[1, 0], 0]}], [[1, 2], {2}, {[[0, 0, 1], 0]}], [[2, 1], {1}, {}]] "First ", 15, " terms of the counting sequence are ", [2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 2, 1] [5, 6, 3, 1] [14, 20, 12, 4, 1] [42, 70, 50, 20, 5, 1] [132, 252, 210, 100, 30, 6, 1] [429, 924, 882, 490, 175, 42, 7, 1] [1430, 3432, 3696, 2352, 980, 280, 56, 8, 1] [4862, 12870, 15444, 11088, 5292, 1764, 420, 72, 9, 1] [16796, 48620, 64350, 51480, 27720, 10584, 2940, 600, 90, 10, 1] [58786, 184756, 267410, 235950, 141570, 60984, 19404, 4620, 825, 110, 11, 1] [208012, 705432, 1108536, 1069640, 707850, 339768, 121968, 33264, 6930, 1100, 132, 12, 1] [742900, 2704156, 4585308, 4803656, 3476330, 1840410, 736164, 226512, 54054, 10010, 1430, 156, 13, 1] [2674440, 10400600, 18929092, 21398104, 16812796, 9733724, 4294290, 1472328, 396396, 84084, 14014, 1820, 182, 14, 1] [9694845, 40116600, 78004500, 94645460, 80242890, 50438388, 24334310, 9202050, 2760615, 660660, 126126, 19110, 2275, 210, 15, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1], [1, 3, 2]}, {[0, 1], [3, 1, 2]}, {[1, 0], [2, 1, 3]}, {[1, 0], [2, 3, 1]}}, " the pattern set ", {[0, 1], [1, 3, 2]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[1], 0]}], [[1], {}, {}], [[1, 0], {1, 2}, {[[0, 1], 0], [[1, 0], 0]}], [[1, 2], {1}, {[[0, 1, 0], 0]}], [[2, 1], {1}, {}]] "First ", 15, " terms of the counting sequence are ", [2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 2, 1] [5, 6, 3, 1] [14, 20, 12, 4, 1] [42, 70, 50, 20, 5, 1] [132, 252, 210, 100, 30, 6, 1] [429, 924, 882, 490, 175, 42, 7, 1] [1430, 3432, 3696, 2352, 980, 280, 56, 8, 1] [4862, 12870, 15444, 11088, 5292, 1764, 420, 72, 9, 1] [16796, 48620, 64350, 51480, 27720, 10584, 2940, 600, 90, 10, 1] [58786, 184756, 267410, 235950, 141570, 60984, 19404, 4620, 825, 110, 11, 1] [208012, 705432, 1108536, 1069640, 707850, 339768, 121968, 33264, 6930, 1100, 132, 12, 1] [742900, 2704156, 4585308, 4803656, 3476330, 1840410, 736164, 226512, 54054, 10010, 1430, 156, 13, 1] [2674440, 10400600, 18929092, 21398104, 16812796, 9733724, 4294290, 1472328, 396396, 84084, 14014, 1820, 182, 14, 1] [9694845, 40116600, 78004500, 94645460, 80242890, 50438388, 24334310, 9202050, 2760615, 660660, 126126, 19110, 2275, 210, 15, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1], [2, 1, 3]}, {[0, 1], [2, 3, 1]}, {[1, 0], [1, 3, 2]}, {[1, 0], [3, 1, 2]}}, " the pattern set ", {[1, 0], [1, 3, 2]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {1, 2}, {[[0, 0], 0]}], [[1, 2], {1}, {[[0, 0, 0], 1], [[0, 1, 0], 0]}], [[2, 1], {1}, {[[0, 0, 0], 1]}]] "First ", 15, " terms of the counting sequence are ", [2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 2, 1] [5, 6, 3, 1] [14, 20, 12, 4, 1] [42, 70, 50, 20, 5, 1] [132, 252, 210, 100, 30, 6, 1] [429, 924, 882, 490, 175, 42, 7, 1] [1430, 3432, 3696, 2352, 980, 280, 56, 8, 1] [4862, 12870, 15444, 11088, 5292, 1764, 420, 72, 9, 1] [16796, 48620, 64350, 51480, 27720, 10584, 2940, 600, 90, 10, 1] [58786, 184756, 267410, 235950, 141570, 60984, 19404, 4620, 825, 110, 11, 1] [208012, 705432, 1108536, 1069640, 707850, 339768, 121968, 33264, 6930, 1100, 132, 12, 1] [742900, 2704156, 4585308, 4803656, 3476330, 1840410, 736164, 226512, 54054, 10010, 1430, 156, 13, 1] [2674440, 10400600, 18929092, 21398104, 16812796, 9733724, 4294290, 1472328, 396396, 84084, 14014, 1820, 182, 14, 1] [9694845, 40116600, 78004500, 94645460, 80242890, 50438388, 24334310, 9202050, 2760615, 660660, 126126, 19110, 2275, 210, 15, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 2], [0, 0, 1]}, {[1, 2], [1, 0, 0]}, {[2, 1], [0, 0, 1]}, {[2, 1], [1, 0, 0]}}, " the pattern set ", {[1, 2], [0, 0, 1]}, " has the scheme ", [[[], {}, {}], [[0], {}, {}], [[1], {1}, {[[0, 1], 0]}], [[0, 0], {1, 2}, {[[1], 0]}], [[0, 1], {2}, {[[0, 1], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 17, 44, 107, 250, 569, 1272, 2807, 6134, 13301, 28660, 61427, 131058, 278513] "First ", 15, " rows of the 0s triangle are: " [1, 1] [1, 4, 1] [1, 9, 6, 1] [1, 16, 18, 8, 1] [1, 25, 40, 30, 10, 1] [1, 36, 75, 80, 45, 12, 1] [1, 49, 126, 175, 140, 63, 14, 1] [1, 64, 196, 336, 350, 224, 84, 16, 1] [1, 81, 288, 588, 756, 630, 336, 108, 18, 1] [1, 100, 405, 960, 1470, 1512, 1050, 480, 135, 20, 1] [1, 121, 550, 1485, 2640, 3234, 2772, 1650, 660, 165, 22, 1] [1, 144, 726, 2200, 4455, 6336, 6468, 4752, 2475, 880, 198, 24, 1] [1, 169, 936, 3146, 7150, 11583, 13728, 12012, 7722, 3575, 1144, 234, 26, 1] [1, 196, 1183, 4368, 11011, 20020, 27027, 27456, 21021, 12012, 5005, 1456, 273, 28, 1] [1, 225, 1470, 5915, 16380, 33033, 50050, 57915, 51480, 35035, 18018, 6825, 1820, 315, 30, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 2], [0, 2, 1]}, {[1, 2], [2, 1, 0]}, {[2, 1], [0, 1, 2]}, {[2, 1], [1, 2, 0]}}, " the pattern set ", {[1, 2], [0, 2, 1]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[2], 0]}], [[1], {1}, {[[0, 1], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 6, 17, 44, 107, 250, 569, 1272, 2807, 6134, 13301, 28660, 61427, 131058, 278513] "First ", 15, " rows of the 0s triangle are: " [1, 1] [1, 4, 1] [1, 6, 9, 1] [1, 8, 18, 16, 1] [1, 10, 30, 40, 25, 1] [1, 12, 45, 80, 75, 36, 1] [1, 14, 63, 140, 175, 126, 49, 1] [1, 16, 84, 224, 350, 336, 196, 64, 1] [1, 18, 108, 336, 630, 756, 588, 288, 81, 1] [1, 20, 135, 480, 1050, 1512, 1470, 960, 405, 100, 1] [1, 22, 165, 660, 1650, 2772, 3234, 2640, 1485, 550, 121, 1] [1, 24, 198, 880, 2475, 4752, 6468, 6336, 4455, 2200, 726, 144, 1] [1, 26, 234, 1144, 3575, 7722, 12012, 13728, 11583, 7150, 3146, 936, 169, 1] [1, 28, 273, 1456, 5005, 12012, 21021, 27456, 27027, 20020, 11011, 4368, 1183, 196, 1] [1, 30, 315, 1820, 6825, 18018, 35035, 51480, 57915, 50050, 33033, 16380, 5915, 1470, 225, 1] "---------------------------------------------" "Overall, we found schemes for ", 16, " out of ", 16, " trivial classes, for a success rate of ", 1.