"There are ", 16, " pattern sets of type ", [3] "They fall into ", 7, " trivial pattern classes." "---------------------------------------------" "For the equivalence class ", {{[0, 0, 0]}}, " the pattern set ", {[0, 0, 0]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 2]}], [[1], {1}, {[[0, 0], 3]}]] "First ", 15, " terms of the counting sequence are ", [2, 7, 33, 192, 1320, 10440, 93240, 927360, 10160640, 121564800, 1576713600, 22034073600, 330032102400, 5274286617600, 89575694208000] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 9, 0] [24, 96, 72, 0, 0] [120, 600, 600, 0, 0, 0] [720, 4320, 5400, 0, 0, 0, 0] [5040, 35280, 52920, 0, 0, 0, 0, 0] [40320, 322560, 564480, 0, 0, 0, 0, 0, 0] [362880, 3265920, 6531840, 0, 0, 0, 0, 0, 0, 0] [3628800, 36288000, 81648000, 0, 0, 0, 0, 0, 0, 0, 0] [39916800, 439084800, 1097712000, 0, 0, 0, 0, 0, 0, 0, 0, 0] [479001600, 5748019200, 15807052800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [6227020800, 80951270400, 242853811200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [87178291200, 1220496076800, 3966612249600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1307674368000, 19615115520000, 68652904320000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 1, 0]}}, " the pattern set ", {[0, 1, 0]}, " has the scheme ", [[[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {1}, {}], [[0, 1], {1, 2}, {[[0, 0], 1]}]] "First ", 15, " terms of the counting sequence are ", [2, 7, 31, 165, 1031, 7423, 60621, 554249, 5611771, 62353011, 754471433, 9876716941, 139097096919, 2097156230471, 33704296561141] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 6, 1] [24, 96, 36, 8, 1] [120, 600, 240, 60, 10, 1] [720, 4320, 1800, 480, 90, 12, 1] [5040, 35280, 15120, 4200, 840, 126, 14, 1] [40320, 322560, 141120, 40320, 8400, 1344, 168, 16, 1] [362880, 3265920, 1451520, 423360, 90720, 15120, 2016, 216, 18, 1] [3628800, 36288000, 16329600, 4838400, 1058400, 181440, 25200, 2880, 270, 20, 1 ] [39916800, 439084800, 199584000, 59875200, 13305600, 2328480, 332640, 39600, 3960, 330, 22, 1] [479001600, 5748019200, 2634508800, 798336000, 179625600, 31933440, 4656960, 570240, 59400, 5280, 396, 24, 1] [6227020800, 80951270400, 37362124800, 11416204800, 2594592000, 467026560, 69189120, 8648640, 926640, 85800, 6864, 468, 26, 1] [87178291200, 1220496076800, 566658892800, 174356582400, 39956716800, 7264857600, 1089728640, 138378240, 15135120, 1441440, 120120, 8736, 546, 28, 1] [1307674368000, 19615115520000, 9153720576000, 2833294464000, 653837184000, 119870150400, 18162144000, 2335132800, 259459200, 25225200, 2162160, 163800, 10920, 630, 30, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 0, 1]}, {[1, 0, 0]}}, " the pattern set ", {[0, 0, 1]}, " has the scheme ", [[[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {1, 2}, {[[1], 0]}], [[0, 1], {2}, {}]] "First ", 15, " terms of the counting sequence are ", [2, 7, 31, 165, 1031, 7423, 60621, 554249, 5611771, 62353011, 754471433, 9876716941, 139097096919, 2097156230471, 33704296561141] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 18, 6, 1] [24, 96, 36, 8, 1] [120, 600, 240, 60, 10, 1] [720, 4320, 1800, 480, 90, 12, 1] [5040, 35280, 15120, 4200, 840, 126, 14, 1] [40320, 322560, 141120, 40320, 8400, 1344, 168, 16, 1] [362880, 3265920, 1451520, 423360, 90720, 15120, 2016, 216, 18, 1] [3628800, 36288000, 16329600, 4838400, 1058400, 181440, 25200, 2880, 270, 20, 1 ] [39916800, 439084800, 199584000, 59875200, 13305600, 2328480, 332640, 39600, 3960, 330, 22, 1] [479001600, 5748019200, 2634508800, 798336000, 179625600, 31933440, 4656960, 570240, 59400, 5280, 396, 24, 1] [6227020800, 80951270400, 37362124800, 11416204800, 2594592000, 467026560, 69189120, 8648640, 926640, 85800, 6864, 468, 26, 1] [87178291200, 1220496076800, 566658892800, 174356582400, 39956716800, 7264857600, 1089728640, 138378240, 15135120, 1441440, 120120, 8736, 546, 28, 1] [1307674368000, 19615115520000, 9153720576000, 2833294464000, 653837184000, 119870150400, 18162144000, 2335132800, 259459200, 25225200, 2162160, 163800, 10920, 630, 30, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 0, 2]}, {[2, 0, 1]}}, " the pattern set ", {[1, 0, 2]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {1, 2}, {[[0, 1], 0]}], [[1, 2], {2}, {}], [[2, 1], {1}, {}]] "First ", 15, " terms of the counting sequence are ", [2, 7, 31, 159, 916, 5859, 41462, 324539, 2810398, 26897153, 283648795, 3280219609, 41351673884, 564705224247, 8303579891143] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 15, 9, 1] [24, 64, 54, 16, 1] [120, 320, 310, 140, 25, 1] [720, 1872, 1890, 1040, 300, 36, 1] [5040, 12684, 12726, 7595, 2800, 567, 49, 1] [40320, 98304, 95984, 58240, 24150, 6496, 980, 64, 1] [362880, 860544, 812592, 484512, 209286, 65394, 13524, 1584, 81, 1] [3628800, 8409600, 7688520, 4439040, 1908900, 636552, 157290, 25920, 2430, 100, 1] [39916800, 90794880, 80708760, 44976360, 18806700, 6339102, 1710786, 345180, 46530, 3575, 121, 1] [479001600, 1073295360, 932171328, 502740480, 202633200, 66870144, 18543756, 4175424, 703890, 79200, 5082, 144, 1] [6227020800, 13784808960, 11750266944, 6163487616, 2394906800, 762284952, 208842348, 49139376, 9428562, 1351350, 128986, 7020, 169, 1] [87178291200, 191094543360, 160467338304, 82290114816, 30960241312, 9472551088, 2509613106, 589672512, 120216096, 19963944, 2466464, 202384, 9464, 196, 1] [1307674368000, 2843255520000, 2358982180800, 1188071604720, 435243463200, 128402790516, 32644281670, 7450809795, 1534979160, 275224950, 40035996, 4312035, 307580, 12495, 225, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 2, 3]}, {[3, 2, 1]}}, " the pattern set ", {[1, 2, 3]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {2}, {}], [[1, 2], {2}, {[[0, 0, 1], 0]}], [[2, 1], {1}, {}]] "First ", 15, " terms of the counting sequence are ", [2, 7, 33, 183, 1118, 7281, 49626, 349999, 2535078, 18758265, 141254655, 1079364105, 8350678170, 65298467487, 515349097713] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [5, 18, 9, 1] [14, 80, 72, 16, 1] [42, 350, 500, 200, 25, 1] [132, 1512, 3150, 2000, 450, 36, 1] [429, 6468, 18522, 17150, 6125, 882, 49, 1] [1430, 27456, 103488, 131712, 68600, 15680, 1568, 64, 1] [4862, 115830, 555984, 931392, 666792, 222264, 35280, 2592, 81, 1] [16796, 486200, 2895750, 6177600, 5821200, 2667168, 617400, 72000, 4050, 100, 1 ] [58786, 2032316, 14707550, 38931750, 46718100, 28174608, 8964648, 1524600, 136125, 6050, 121, 1] [208012, 8465184, 73163376, 235320800, 350385750, 269096256, 112698432, 26345088, 3430350, 242000, 8712, 144, 1] [742900, 35154028, 357654024, 1373845616, 2485575950, 2368607670, 1263257424, 388694592, 69567498, 7157150, 408980, 12168, 169, 1] [2674440, 145608400, 1722547372, 7788909856, 16829608796, 19486915448, 12895752870, 5053029696, 1190377188, 168336168, 14028014, 662480, 16562, 196, 1] [9694845, 601749000, 8190472500, 43063684300, 109531544850, 151466479164, 121793221550, 59215191750, 17764557525, 3306603300, 378756378, 26085150, 1035125, 22050, 225, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1, 2]}, {[0, 2, 1]}, {[1, 2, 0]}, {[2, 1, 0]}}, " the pattern set ", {[0, 1, 2]}, " has the scheme ", [[[], {}, {}], [[0], {}, {}], [[1], {1}, {}], [[0, 0], {1}, {}], [[0, 1], {2}, {[[0, 1], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 7, 31, 159, 921, 5988, 43632, 355491, 3223729, 32329668, 355979064, 4273100846, 55555511298, 777797216472, 11667035805840] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [6, 15, 9, 1] [24, 64, 54, 16, 1] [120, 325, 310, 140, 25, 1] [720, 1956, 1935, 1040, 300, 36, 1] [5040, 13699, 13671, 7805, 2800, 567, 49, 1] [40320, 109600, 109564, 63616, 24850, 6496, 980, 64, 1] [362880, 986409, 986364, 574896, 230706, 67284, 13524, 1584, 81, 1] [3628800, 9864100, 9864045, 5753280, 2324700, 704592, 161700, 25920, 2430, 100, 1] [39916800, 108505111, 108505045, 63293505, 25611300, 7847532, 1895124, 354420, 46530, 3575, 121, 1] [479001600, 1302061344, 1302061266, 759534160, 307417275, 94431744, 23168376, 4618944, 721710, 79200, 5082, 144, 1] [6227020800, 16926797485, 16926797394, 9873962956, 3996581875, 1228249737, 302547960, 61631856, 10401534, 1383525, 128986, 7020, 169, 1] [87178291200, 236975164804, 236975164699, 138235509776, 55952432536, 17196927748, 4239536301, 868735296, 150774624, 21945924, 2521519, 202384, 9464, 196, 1] [1307674368000, 3554627472075, 3554627471955, 2073532688045, 839286984900, 257956922223, 63603064525, 13050353745, 2283704280, 344218875, 43834791, 4402125, 307580, 12495, 225, 1] "---------------------------------------------" "For the equivalence class ", {{[1, 3, 2]}, {[2, 1, 3]}, {[2, 3, 1]}, {[3, 1, 2]}}, " the pattern set ", {[1, 3, 2]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {}], [[1], {}, {}], [[1, 0], {2}, {}], [[1, 2], {1}, {[[0, 1, 0], 0]}], [[2, 1], {1}, {}]] "First ", 15, " terms of the counting sequence are ", [2, 7, 33, 183, 1118, 7281, 49626, 349999, 2535078, 18758265, 141254655, 1079364105, 8350678170, 65298467487, 515349097713] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 4, 1] [5, 18, 9, 1] [14, 80, 72, 16, 1] [42, 350, 500, 200, 25, 1] [132, 1512, 3150, 2000, 450, 36, 1] [429, 6468, 18522, 17150, 6125, 882, 49, 1] [1430, 27456, 103488, 131712, 68600, 15680, 1568, 64, 1] [4862, 115830, 555984, 931392, 666792, 222264, 35280, 2592, 81, 1] [16796, 486200, 2895750, 6177600, 5821200, 2667168, 617400, 72000, 4050, 100, 1 ] [58786, 2032316, 14707550, 38931750, 46718100, 28174608, 8964648, 1524600, 136125, 6050, 121, 1] [208012, 8465184, 73163376, 235320800, 350385750, 269096256, 112698432, 26345088, 3430350, 242000, 8712, 144, 1] [742900, 35154028, 357654024, 1373845616, 2485575950, 2368607670, 1263257424, 388694592, 69567498, 7157150, 408980, 12168, 169, 1] [2674440, 145608400, 1722547372, 7788909856, 16829608796, 19486915448, 12895752870, 5053029696, 1190377188, 168336168, 14028014, 662480, 16562, 196, 1] [9694845, 601749000, 8190472500, 43063684300, 109531544850, 151466479164, 121793221550, 59215191750, 17764557525, 3306603300, 378756378, 26085150, 1035125, 22050, 225, 1] "---------------------------------------------" "Overall, we found schemes for ", 7, " out of ", 7, " trivial classes, for a success rate of ", 1.