My integer sequences in OEIS
Published:
I have submitted few sequences to the OEIS, most of which are connected to my work on applying the Kauffman bracket polynomial to knot shadows.
0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
0, 1, 7, 19, 39, 71, 123, 211, 367, 655, 1203, 2267, 4359, 8503, 16747, 33187, 66015, 131615, 262755, 524971, 1049335, 2097991, 4195227, 8389619, 16778319, 33555631, 67110163, 134219131, 268436967, 536872535, 1073743563, 2147485507
1, 5, 19, 62, 184, 512, 1360, 3488, 8704, 21248, 50944, 120320, 280576, 647168, 1478656, 3350528, 7536640, 16842752, 37421056, 82706432, 181927936, 398458880, 869269504, 1889533952, 4093640704, 8841592832, 19042140160, 40902852608
0, 1, 0, 3, 4, 1, 0, 9, 24, 22, 8, 1, 0, 27, 108, 171, 136, 57, 12, 1, 0, 81, 432, 972, 1200, 886, 400, 108, 16, 1, 0, 243, 1620, 4725, 7920, 8430, 5944, 2810, 880, 175, 20, 1, 0, 729, 5832, 20898, 44280, 61695, 59472, 40636, 19824, 6855, 1640, 258, 24, 1
0, 0, 1, 0, 1, 2, 1, 0, 4, 7, 4, 1, 0, 12, 26, 19, 6, 1, 0, 32, 88, 88, 39, 8, 1, 0, 80, 272, 360, 230, 71, 10, 1, 0, 192, 784, 1312, 1140, 532, 123, 12, 1, 0, 448, 2144, 4368, 4872, 3164, 1162, 211, 14, 1, 0, 1024, 5632, 13568, 18592, 15680, 8176, 2480, 367, 16, 1, 0, 2304, 14336, 39936, 65088, 67872, 46368, 20304, 5262, 655, 18, 1
0, 0, 1, 0, 1, 2, 1, 0, 2, 6, 6, 2, 0, 3, 13, 22, 18, 7, 1, 0, 4, 23, 56, 75, 60, 29, 8, 1, 0, 5, 36, 115, 215, 261, 215, 121, 45, 10, 1, 0, 6, 52, 206, 495, 806, 938, 798, 496, 220, 66, 12, 1, 0, 7, 71, 336, 987, 2016, 3031, 3452, 3010, 2003, 1001, 364, 91, 14, 1
- A300401: (square array read by antidiagonals)
0, 1, 1, 2, 2, 2, 3, 4, 4, 3, 4, 7, 8, 7, 4, 5, 11, 14, 14, 11, 5, 6, 16, 22, 24, 22, 16, 6, 7, 22, 32, 37, 37, 32, 22, 7, 8, 29, 44, 53, 56, 53, 44, 29, 8, 9, 37, 58, 72, 79, 79, 72, 58, 37, 9, 10, 46, 74, 94, 106, 110, 106, 94, 74, 46, 10, 11, 56, 92, 119, 137, 146, 146, 137, 119, 92, 56, 11
1, 2, 7, 26, 88, 272, 784, 2144, 5632, 14336, 35584, 86528, 206848, 487424, 1134592, 2613248, 5963776, 13500416, 30343168, 67764224, 150470656, 332398592, 730857472, 1600126976, 3489660928, 7583301632, 16424894464, 35467034624, 76369887232, 164014063616
0, 0, 1, 0, 1, 1, 0, 2, 2, 0, 3, 4, 1, 0, 4, 7, 4, 1, 0, 5, 11, 10, 5, 1, 0, 6, 16, 20, 15, 6, 1, 0, 7, 22, 35, 35, 21, 7, 1, 0, 8, 29, 56, 70, 56, 28, 8, 1, 0, 9, 37, 84, 126, 126, 84, 36, 9, 1, 0, 10, 46, 120, 210, 252, 210, 120, 45, 10, 1, 0, 11, 56, 165, 330, 462, 462, 330, 165, 55, 11, 1
0, 1, 2, 1, 0, 3, 4, 1, 0, 5, 8, 3, 0, 7, 14, 9, 2, 0, 9, 22, 21, 10, 2, 0, 11, 32, 41, 30, 12, 2, 0, 13, 44, 71, 70, 42, 14, 2, 0, 15, 58, 113, 140, 112, 56, 16, 2, 0, 17, 74, 169, 252, 252, 168, 72, 18, 2, 0, 19, 92, 241, 420, 504, 420, 240, 90, 20, 2
1, 8, 16, 25, 35, 46, 58, 71, 85, 100, 116, 133, 151, 170, 190, 211, 233, 256, 280, 305, 331, 358, 386, 415, 445, 476, 508, 541, 575, 610, 646, 683, 721, 760, 800, 841, 883, 926, 970, 1015, 1061, 1108, 1156, 1205, 1255, 1306, 1358, 1411, 1465, 1520, 1576
- A303273: (array read by antidiagonals)
1, 1, 1, 1, 2, 2, 1, 3, 4, 4, 1, 4, 6, 7, 7, 1, 5, 8, 10, 11, 11, 1, 6, 10, 13, 15, 16, 16, 1, 7, 12, 16, 19, 21, 22, 22, 1, 8, 14, 19, 23, 26, 28, 29, 29, 1, 9, 16, 22, 27, 31, 34, 36, 37, 37, 1, 10, 18, 25, 31, 36, 40, 43, 45, 46, 46, 1, 11, 20, 28, 35, 41, 46, 50, 53, 55, 56, 56
12, 168, 2784, 48912, 874416, 15709488, 282620784, 5086424112, 91551884016, 1647915162288, 29662379171184, 533922356331312, 9610600070213616, 172990789545095088, 3113834153217961584, 56049014464954558512, 1008882258904338303216, 18159880652953870707888
1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 4, 4, 1, 1, 3, 8, 7, 5, 1, 1, 4, 10, 17, 11, 6, 1, 1, 4, 16, 26, 31, 16, 7, 1, 1, 5, 19, 47, 56, 51, 22, 8, 1, 1, 5, 27, 65, 112, 106, 78, 29, 9, 1, 1, 6, 31, 101, 176, 232, 183, 113, 37, 10, 1, 1, 6, 41, 131, 296, 407, 435, 295, 157, 46, 11, 1
0, 0, 0, 1, 0, 1, 2, 1, 0, 5, 8, 3, 0, 16, 30, 16, 2, 0, 45, 104, 81, 24, 2, 0, 121, 340, 356, 170, 35, 2, 0, 320, 1068, 1411, 932, 315, 48, 2, 0, 841, 3262, 5209, 4396, 2079, 532, 63, 2, 0, 2205, 9760, 18281, 18784, 11440, 4144, 840, 80, 2, 0, 5776, 28746, 61786, 74838, 55809, 26226, 7602, 1260, 99, 2
0, 1, 3, 3, 1, 0, 7, 14, 9, 2, 0, 13, 37, 43, 26, 8, 1, 0, 19, 72, 129, 141, 98, 42, 10, 1, 0, 25, 119, 291, 463, 504, 378, 192, 63, 12, 1, 0, 31, 178, 553, 1156, 1716, 1848, 1452, 825, 330, 88, 14, 1, 0, 37, 249, 939, 2432, 4576, 6435, 6864, 5577, 3432, 1573, 520, 117, 16, 1
2, 3, 0, 1, 4, 5, 6, 7, 10, 11, 8, 9, 12, 13, 14, 15, 18, 19, 16, 17, 20, 21, 22, 23, 26, 27, 24, 25, 28, 29, 30, 31, 34, 35, 32, 33, 36, 37, 38, 39, 42, 43, 40, 41, 44, 45, 46, 47, 50, 51, 48, 49, 52, 53, 54, 55, 58, 59, 56, 57, 60, 61, 62, 63, 66, 67, 64
0, 1, 0, 1, 0, 1, 1, 0, 3, 0, 3, 3, 1, 0, 9, 11, 1, 0, 17, 22, 9, 1
0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 1, 0, 3, 0, 2, 0, 1, 9, 0, 8, 0, 3, 0, 1, 11, 0, 21, 0, 12, 0, 4, 0, 1, 54, 0, 68, 0, 32, 0, 1, 0, 1, 148, 228, 0, 124, 0, 44, 7, 0, 1, 619, 0, 900, 0, 461, 0, 162, 0, 34
0, 0, 1, 0, 2, 1, 5, 8, 22, 51, 182, 562
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 4, 4, 1, 1, 5, 5, 5, 5, 1, 1, 6, 6, 6, 6, 6, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 8, 8, 8, 8, 8, 8, 8, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 1, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 1
1, 1, 1, 2, 1, 1, 5, 2, 1, 1, 14, 5, 2, 1, 1, 51, 15, 5, 2, 1, 1, 267, 67, 15, 5, 2, 1, 1, 2328, 504, 77, 15, 5, 2, 1, 1, 56092, 9310, 684, 83, 15, 5, 2, 1, 1, 10494213, 1396077, 34297, 860, 87, 15, 5, 2, 1, 1, 49487367289, 5937876645,
1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 3, 1, 1, 1, 5, 5, 5, 5, 1, 1, 3, 15, 5, 15, 3, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 1, 7, 7, 35, 7, 7, 1, 1, 1, 9, 9, 21, 63, 63, 21, 9, 9, 1, 1, 5, 45, 15, 105, 63, 105, 15, 45, 5, 1, 1, 11, 55, 165, 165, 231, 231, 165, 165, 55, 11, 1
1, 2, 2, 4, 2, 4, 8, 8, 8, 8, 16, 4, 8, 4, 16, 32, 32, 16, 16, 32, 32, 64, 32, 64, 16, 64, 32, 64, 128, 128, 128, 128, 128, 128, 128, 128, 256, 32, 64, 32, 128, 32, 64, 32, 256, 512, 512, 128, 128, 256, 256, 128, 128, 512, 512
5, 5, 2, 2, 8, 4, 7, 4, 9, 8, 3, 0, 7, 9, 3, 3, 9, 8, 4, 0, 2, 2, 5, 1, 6, 3, 2, 2, 7, 9, 5, 9, 7, 4, 3, 8, 0, 9, 2, 8, 9, 5, 8, 3, 3, 8, 3, 5, 9, 3, 0, 7, 6, 4, 2, 3, 5, 5, 7, 2, 9, 8, 3, 9, 8, 7, 6, 4, 3, 3, 0, 4, 6, 1, 6, 1, 4, 2, 7, 1, 8, 4, 6, 7, 1, 8, 3
0, -1, 1, -1, 0, 1, -3, -3, 3, 3, -1, -1, 0, 1, 1, -5, -15, -5, 5, 15, 5, -3, -3, -15, 0, 15, 3, 3, -7, -35, -63, -35, 35, 63, 35, 7, -1, -3, -7, -7, 0, 7, 7, 3, 1, -9, -63, -45, -63, -63, 63, 63, 45, 63, 9, -5, -5, -135, -15, -105, 0, 105, 15, 135, 5, 5
1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 2, 1, 1, 1, 2, 16, 16, 8, 8, 16, 16, 16, 4, 16, 1, 16, 4, 16, 64, 64, 64, 64, 64, 64, 64, 64, 16, 8, 8, 8, 1, 8, 8, 8, 16, 256, 256, 64, 64, 128, 128, 64, 64, 256, 256, 256, 32, 256, 16, 128, 1, 128, 16, 256, 32, 256
1, 1, -1, 1, 0, 1, 1, 1, 0, -1, 1, 2, 0, 0, 1, 1, 3, 1, 0, 0, -1, 1, 4, 3, 0, 0, 0, 1, 1, 5, 6, 1, 0, 0, 0, -1, 1, 6, 10, 4, 0, 0, 0, 0, 1, 1, 7, 15, 10, 1, 0, 0, 0, 0, -1, 1, 8, 21, 20, 5, 0, 0, 0, 0, 0, 1, 1, 9, 28, 35, 15, 1, 0, 0, 0, 0, 0, -1, 1, 10, 36, 56, 35, 6, 0, 0, 0, 0, 0, 0, 1
- A320530: (square array read by antidiagonals)
1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 0, 4, 7, 3, 1, 0, 7, 26, 16, 4, 1, 0, 11, 88, 90, 29, 5, 1, 0, 16, 272, 459, 220, 46, 6, 1, 0, 22, 784, 2133, 1504, 440, 67, 7, 1, 0, 29, 2144, 9234, 9344, 3775, 774, 92, 8, 1, 0, 37, 5632, 37908, 54016, 29375, 7992, 1246, 121, 9, 1
- A320531: (square array read by antidiagonals)
0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 3, 4, 1, 0, 0, 4, 12, 6, 1, 0, 0, 5, 32, 27, 8, 1, 0, 0, 6, 80, 108, 48, 10, 1, 0, 0, 7, 192, 405, 256, 75, 12, 1, 0, 0, 8, 448, 1458, 1280, 500, 108, 14, 1, 0, 0, 9, 1024, 5103, 6144, 3125, 864, 147, 16, 1, 0
12, 72, 672, 6048, 55488, 511872, 4738560, 43943424, 407890944, 3787941888, 35186122752, 326885842944, 3037038034944, 28217571901440, 262178452930560, 2436006721486848, 22634041833160704, 210303674768424960, 1954034324430913536, 18155901427591938048
0, 1, 1, 3, 10, 3, 4, 11, 11, 4, 11, 32, 26, 32, 11, 15, 43, 37, 37, 43, 15, 41, 118, 100, 106, 100, 118, 41, 56, 161, 137, 143, 143, 137, 161, 56, 153, 440, 374, 392, 386, 392, 374, 440, 153, 209, 601, 511, 535, 529, 529, 535, 511, 601, 209
4, 2, 8, 10, 28, 38, 104, 142, 388, 530, 1448, 1978, 5404, 7382, 20168, 27550, 75268, 102818, 280904, 383722, 1048348, 1432070, 3912488, 5344558, 14601604, 19946162, 54493928, 74440090, 203374108, 277814198, 759002504, 1036816702, 2832635908, 3869452610
3, 9, 4, 3, 3, 7, 5, 6, 7, 2, 9, 7, 4, 0, 6, 4, 4, 1, 1, 2, 7, 2, 8, 7, 1, 9, 5, 1, 2, 5, 4, 8, 9, 3, 6, 3, 9, 1, 1, 9, 0, 0, 4, 3, 7, 8, 1, 7, 5, 3, 1, 7, 1, 9, 0, 0, 4, 6, 5, 0, 5, 8, 1, 6, 2, 0, 9, 9, 4, 4, 1, 8, 0, 7, 5, 7, 3, 3, 3, 3, 6, 4, 2, 3, 4, 2, 8
0, 1, 1, 1, 4, 1, 3, 9, 9, 3, 13, 44, 30, 44, 13, 35, 115, 90, 90, 115, 35, 16, 53, 40, 46, 40, 53, 16, 131, 433, 330, 366, 366, 330, 433, 131, 179, 592, 450, 504, 486, 504, 450, 592, 179, 163, 539, 410, 458, 446, 446, 458, 410, 539, 163, 668, 2209, 1680, 1878, 1824, 1842, 1824, 1878, 1680, 2209, 668
4, 2, 3, 8, 36, 96, 44, 360, 492, 448, 1836, 5016, 2284, 18720, 25572, 23288, 95436, 260736, 118724, 973080, 1329252, 1210528, 4960836, 13553256, 6171364, 50581440, 69095532, 62924168, 257868036, 704508576, 320792204, 2629261800, 3591638412, 3270846208
2, 7, 17, 33, 57, 93, 149, 241, 401, 693, 1245, 2313, 4409, 8557, 16805, 33249, 66081, 131685, 262829, 525049, 1049417, 2098077, 4195317, 8389713, 16778417, 33555733, 67110269, 134219241, 268437081, 536872653, 1073743685, 2147485633, 4294969409, 8589936837
1, 5, 13, 33, 73, 141, 245, 393, 593, 853, 1181, 1585, 2073, 2653, 3333, 4121, 5025, 6053, 7213, 8513, 9961, 11565, 13333, 15273, 17393, 19701, 22205, 24913, 27833, 30973, 34341, 37945, 41793, 45893, 50253, 54881, 59785, 64973, 70453, 76233, 82321, 88725
1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1
- A321126: (square array read by antidiagonals)
1, 2, 2, 3, 2, 3, 4, 3, 3, 4, 5, 4, 3, 4, 5, 6, 5, 4, 4, 5, 6, 7, 6, 5, 5, 5, 6, 7, 8, 7, 6, 6, 6, 6, 7, 8, 9, 8, 7, 7, 7, 7, 7, 8, 9, 10, 9, 8, 8, 8, 8, 8, 8, 9, 10, 11, 10, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 11, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 13, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 13
- A321127: (square array read by antidiagonals)
0, 1, 0, 2, 2, 0, 5, 8, 3, 0, 10, 24, 21, 8, 1, 0, 17, 56, 80, 64, 30, 8, 1, 0, 26, 110, 220, 270, 220, 122, 45, 10, 1, 0, 37, 192, 495, 820, 952, 804, 497, 220, 66, 12, 1, 0, 50, 308, 973, 2030, 3059, 3472, 3017, 2004, 1001, 364, 91, 14, 1
1, 5, 13, 33, 73, 141, 245, 393, 593, 853, 1181, 1585, 2073, 2653, 3333, 4121, 5025, 6053, 7213, 8513, 9961, 11565, 13333, 15273, 17393, 19701, 22205, 24913, 27833, 30973, 34341, 37945, 41793, 45893, 50253, 54881, 59785, 64973, 70453, 76233, 82321, 88725
1, 5, 25, 69, 145, 261, 425, 645, 929, 1285, 1721, 2245, 2865, 3589, 4425, 5381, 6465, 7685, 9049, 10565, 12241, 14085, 16105, 18309, 20705, 23301, 26105, 29125, 32369, 35845, 39561, 43525, 47745, 52229, 56985, 62021, 67345, 72965, 78889, 85125, 91681, 98565
3, 11, 21, 35, 55, 83, 121, 171, 235, 315, 413, 531, 671, 835, 1025, 1243, 1491, 1771, 2085, 2435, 2823, 3251, 3721, 4235, 4795, 5403, 6061, 6771, 7535, 8355, 9233, 10171, 11171, 12235, 13365, 14563, 15831, 17171, 18585, 20075, 21643, 23291, 25021, 26835
- A322596: (square array read by antidiagonals)
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 3, 4, 3, 1, 1, 1, 3, 5, 5, 3, 1, 1, 1, 4, 7, 9, 7, 4, 1, 1, 1, 4, 10, 14, 14, 10, 4, 1, 1, 1, 5, 12, 21, 26, 21, 12, 5, 1, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 1, 6, 19, 42, 66, 77, 66, 42, 19, 6, 1, 1, 1, 6, 22, 55, 99, 132, 132, 99, 55, 22, 6, 1, 1
1, 7, 17, 39, 81, 151, 257, 407, 609, 871, 1201, 1607, 2097, 2679, 3361, 4151, 5057, 6087, 7249, 8551, 10001, 11607, 13377, 15319, 17441, 19751, 22257, 24967, 27889, 31031, 34401, 38007, 41857, 45959, 50321, 54951, 59857, 65047, 70529, 76311, 82401, 88807
1, 3, 1, 11, 2, 1, 25, 35, 5, 1, 137, 15, 17, 3, 1, 49, 203, 49, 35, 7, 1, 363, 469, 967, 28, 23, 4, 1, 761, 29531, 801, 1069, 27, 39, 9, 1, 7129, 6515, 4523, 285, 3013, 75, 145, 5, 1, 7381, 177133, 84095, 341693, 8591, 7513, 605, 44, 11, 1, 83711, 190553, 341747, 139381, 242537, 1903, 10831, 33, 35, 6, 1
1, 2, 1, 6, 1, 1, 12, 12, 2, 1, 60, 4, 4, 1, 1, 20, 45, 8, 6, 2, 1, 140, 90, 120, 3, 3, 1, 1, 280, 5040, 80, 80, 2, 4, 2, 1, 2520, 1008, 378, 16, 144, 4, 12, 1, 1, 2520, 25200, 6048, 15120, 288, 240, 24, 3, 2, 1, 27720, 25200, 21600, 5040, 6048, 40, 240, 1, 2, 1, 1