For words avoiding the pattern, [0, 1, 1, 1, 0], with spacings <=, 0 4 1 + t the generating function is, - ----------------- 5 4 t - 1 - t + 2 t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 433, 837, 1618, 3128, 6047, 11690, 22599, 43688, 84457, 163271, 315633, 610177, 1179585, 2280356, 4408350, 8522156, 16474904, 31849037, 61570080, 119026354, 230099960, 444825787] the asympt. constant is, 1.933184982 For words avoiding the pattern, [0, 0, 0, 0, 0], with spacings <=, 0 2 4 3 t + t + t + 1 + t the generating function is, - ------------------------- 2 4 3 5 t + t + t + t - 1 + t the first , 30, terms are , [2, 4, 8, 16, 31, 61, 120, 236, 464, 912, 1793, 3525, 6930, 13624, 26784, 52656, 103519, 203513, 400096, 786568, 1546352, 3040048, 5976577, 11749641, 23099186, 45411804, 89277256, 175514464, 345052351, 678355061] the asympt. constant is, 1.965948237 For words avoiding the pattern, [1, 0, 0, 0, 0], with spacings <=, 0 1 the generating function is, ------------ 5 t + 1 - 2 t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 432, 833, 1606, 3096, 5968, 11504, 22175, 42744, 82392, 158816, 306128, 590081, 1137418, 2192444, 4226072, 8146016, 15701951, 30266484, 58340524, 112454976, 216763936, 417825921] the asympt. constant is, 1.927561975 For words avoiding the pattern, [0, 1, 0, 0, 0], with spacings <=, 0 4 1 + t the generating function is, - ----------------- 5 4 t - 1 - t + 2 t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 433, 837, 1618, 3128, 6047, 11690, 22599, 43688, 84457, 163271, 315633, 610177, 1179585, 2280356, 4408350, 8522156, 16474904, 31849037, 61570080, 119026354, 230099960, 444825787] the asympt. constant is, 1.933184982 For words avoiding the pattern, [1, 1, 0, 0, 0], with spacings <=, 0 1 the generating function is, ------------ 5 t + 1 - 2 t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 432, 833, 1606, 3096, 5968, 11504, 22175, 42744, 82392, 158816, 306128, 590081, 1137418, 2192444, 4226072, 8146016, 15701951, 30266484, 58340524, 112454976, 216763936, 417825921] the asympt. constant is, 1.927561975 For words avoiding the pattern, [1, 0, 1, 0, 0], with spacings <=, 0 1 the generating function is, ------------ 5 t + 1 - 2 t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 432, 833, 1606, 3096, 5968, 11504, 22175, 42744, 82392, 158816, 306128, 590081, 1137418, 2192444, 4226072, 8146016, 15701951, 30266484, 58340524, 112454976, 216763936, 417825921] the asympt. constant is, 1.927561975 For words avoiding the pattern, [0, 1, 1, 0, 0], with spacings <=, 0 4 1 + t the generating function is, - ----------------- 5 4 t - 1 - t + 2 t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 433, 837, 1618, 3128, 6047, 11690, 22599, 43688, 84457, 163271, 315633, 610177, 1179585, 2280356, 4408350, 8522156, 16474904, 31849037, 61570080, 119026354, 230099960, 444825787] the asympt. constant is, 1.933184982 For words avoiding the pattern, [0, 0, 1, 0, 0], with spacings <=, 0 3 4 t + t + 1 the generating function is, - ---------------------- 4 5 3 t + t - 1 + 2 t - t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 225, 437, 849, 1649, 3202, 6217, 12071, 23438, 45510, 88368, 171586, 333171, 646922, 1256136, 2439055, 4735945, 9195847, 17855697, 34670640, 67320433, 130716961, 253814826, 492835556] the asympt. constant is, 1.941713034 For words avoiding the pattern, [1, 0, 0, 1, 0], with spacings <=, 0 3 t + 1 the generating function is, ------------------------- 4 5 3 -2 t + t + 1 - 2 t + t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 225, 436, 845, 1637, 3172, 6146, 11909, 23075, 44711, 86633, 167863, 325256, 630226, 1221144, 2366125, 4584673, 8883398, 17212733, 33351899, 64623621, 125216632, 242623433, 470114310] the asympt. constant is, 1.937629450 For words avoiding the pattern, [0, 1, 0, 1, 0], with spacings <=, 0 2 4 t + 1 + t the generating function is, - ----------------------------- 3 5 4 2 2 t + t - 1 - t + 2 t - t the first , 30, terms are , [2, 4, 8, 16, 31, 60, 117, 228, 444, 865, 1685, 3282, 6393, 12453, 24257, 47250, 92038, 179280, 349218, 680239, 1325032, 2581019, 5027546, 9793116, 19075931, 37157851, 72379476, 140987393, 274628197, 534946033] the asympt. constant is, 1.947891873 The low champion is, [1, 0, 0, 0, 0], with asympt. constant, 1.927561975 The high champion is, [0, 0, 0, 0, 0], with asympt. constant, 1.965948237 For words avoiding the pattern, [0, 1, 1, 1, 0], with spacings <=, 1 24 16 15 14 13 12 the generating function is, - (t - 6 t - 2 t - 2 t + 2 t - t 11 10 8 7 5 4 / 25 24 17 16 - 2 t - t + 10 t + 2 t + t + t + 1) / (t - t - 5 t + 3 t / 14 13 12 10 9 8 7 6 4 + 3 t - 2 t - t + t + 8 t - 6 t - 2 t + 2 t - t + 2 t - 1) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 421, 790, 1478, 2760, 5159, 9641, 18001, 33601, 62763, 117229, 218989, 409127, 764307, 1427836, 2667541, 4983676, 9310693, 17394741, 32497636, 60713235, 113427050, 211909343] the asympt. constant is, 1.868239168 For words avoiding the pattern, [0, 0, 0, 0, 0], with spacings <=, 1 3 6 11 8 16 10 the generating function is, - (-1 - 2 t - t - 6 t + 2 t - 11 t + t + t 15 14 4 7 2 5 9 / + 2 t + t - 4 t - 6 t - 2 t - 3 t - 7 t ) / ( / 12 17 10 3 8 7 16 9 5 2 t - t + t - 7 t - 2 t - t + 1 - 5 t + t - 5 t - 4 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 61, 120, 236, 456, 880, 1716, 3345, 6517, 12692, 24706, 48113, 93688, 182432, 355207, 691581, 1346652, 2622188, 5105815, 9941828, 19358157, 37693373, 73394861, 142911048, 278269814, 541833681] the asympt. constant is, 1.947153929 For words avoiding the pattern, [1, 0, 0, 0, 0], with spacings <=, 1 the generating function is, 7 1 + 2 t - ------------------------------------------------------------- 17 16 9 8 12 10 5 7 t - t - 8 t + 4 t + 3 t + 3 t - t + 2 t - 2 t - 1 the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 424, 804, 1522, 2881, 5444, 10284, 19417, 36659, 69173, 130532, 246290, 464699, 876722, 1654047, 3120482, 5887015, 11106070, 20952031, 39526573, 74567910, 140673833, 265383897] the asympt. constant is, 1.886514351 For words avoiding the pattern, [0, 1, 0, 0, 0], with spacings <=, 1 15 16 11 7 4 13 the generating function is, - (1 + t - 3 t - 3 t + t + t - 3 t 21 8 9 10 14 / 12 8 9 4 + 2 t + 9 t - 4 t - 7 t + t ) / (-3 t + 2 t - 7 t + 12 t - t / 5 22 16 21 17 11 7 14 15 + t + 2 t + 4 t - 2 t - 3 t - 1 - 4 t - t - 4 t + t 13 + 3 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 423, 798, 1509, 2852, 5398, 10216, 19323, 36543, 69161, 130888, 247678, 468697, 886881, 1678180, 3175629, 6009303, 11371187, 21517361, 40716837, 77047375, 145795221, 275885481] the asympt. constant is, 1.892277618 For words avoiding the pattern, [1, 1, 0, 0, 0], with spacings <=, 1 15 12 10 7 5 / 20 17 the generating function is, (t + t + t - 3 t - t - 1) / (t + 5 t / 16 15 14 13 12 11 9 8 7 - 2 t + 2 t + 6 t - 2 t + 2 t - 2 t - 10 t + 6 t - 3 t 6 5 + 2 t - 2 t + 2 t - 1) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 422, 793, 1486, 2780, 5184, 9668, 18007, 33526, 62344, 115900, 215364, 400121, 743150, 1380196, 2562946, 4758988, 8835847, 16404694, 30455516, 56539988, 104962162, 194852375] the asympt. constant is, 1.856309300 For words avoiding the pattern, [1, 0, 1, 0, 0], with spacings <=, 1 the generating function is, - ( 6 15 16 7 2 3 4 5 11 8 10 -1 - t - 2 t + t + t - 4 t - t - t - t - 2 t + t - 4 t + t ) / 19 26 2 25 13 10 14 18 15 6 / (-t + t - t + t - 3 t + 12 t + 1 - t - 7 t - 2 t - t / 12 9 11 5 20 17 3 4 7 8 21 - t + 9 t + 6 t + t - t + t - 5 t - t - t + t - 3 t + t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 416, 774, 1442, 2686, 4984, 9250, 17143, 31748, 58687, 108484, 200528, 370629, 684764, 1265080, 2336860, 4316280, 7971488, 14721922, 27188174, 50209612, 92721295, 171225089] the asympt. constant is, 1.846577102 For words avoiding the pattern, [0, 1, 1, 0, 0], with spacings <=, 1 24 19 17 16 15 13 11 the generating function is, - (t + 2 t + t - 7 t - t + t - 8 t 10 8 7 5 4 / 25 24 20 19 18 - t + 12 t + 3 t + t + t + 1) / (t - t + 2 t - 2 t + t / 17 16 15 12 11 10 9 8 7 6 - 7 t + 5 t + t - 8 t + 6 t + t + 10 t - 6 t - 3 t + 2 t 4 - t + 2 t - 1) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 419, 782, 1454, 2703, 5030, 9360, 17399, 32336, 60166, 111969, 208451, 388079, 722461, 1344946, 2503986, 4661980, 8679543, 16159182, 30083735, 56007063, 104268980, 194119066] the asympt. constant is, 1.861705304 For words avoiding the pattern, [0, 0, 1, 0, 0], with spacings <=, 1 3 4 6 15 19 8 10 the generating function is, - (1 + t + t + 5 t - 8 t - t + 9 t + 4 t 16 13 22 7 18 20 17 23 12 14 - 9 t - 7 t + 2 t + 2 t - 4 t - t - 6 t + t - 3 t - 7 t / 6 7 17 19 13 14 12 15 16 ) / (-5 t + 8 t - 1 - 6 t - 4 t + t - 3 t + t - 2 t - 3 t / 5 24 9 4 3 18 8 10 11 20 22 23 + t + t + 6 t + t - t - 2 t - 5 t + t + 3 t - t - t + t + 2 t) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 225, 425, 806, 1525, 2890, 5481, 10393, 19757, 37538, 71395, 135747, 258126, 490801, 932984, 1773627, 3371143, 6407857, 12179461, 23150045, 44002995, 83639733, 158983662, 302196856] the asympt. constant is, 1.900810612 For words avoiding the pattern, [1, 0, 0, 1, 0], with spacings <=, 1 the generating function is, - ( 18 15 12 9 8 7 6 5 3 / 10 2 t + 2 t + t - 3 t - t - 2 t - 5 t - t - t - 1) / (-6 t / 13 17 19 16 6 15 21 22 + t - 2 t - 5 t + 4 t + 7 t + 3 t - 3 t - 4 t + 2 t + 1 7 5 8 9 3 4 18 14 12 - 8 t + 2 t - 3 t + 12 t + t - 2 t - 2 t - t + 3 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 225, 425, 802, 1514, 2861, 5394, 10172, 19221, 36326, 68593, 129517, 244615, 462000, 872327, 1647114, 3110470, 5873939, 11091969, 20945435, 39553543, 74692997, 141047459, 266349195] the asympt. constant is, 1.888376733 For words avoiding the pattern, [0, 1, 0, 1, 0], with spacings <=, 1 26 24 22 21 20 19 18 the generating function is, - (t + 2 t - 3 t + t - 5 t - t + 3 t 17 16 15 14 13 12 11 10 9 - 2 t + 4 t + 3 t - 12 t - 3 t - 15 t - 4 t + 11 t + 3 t 8 7 6 5 4 2 / 21 6 + 15 t + 4 t + 3 t + t + 4 t + t + 1) / (-1 - 5 t + 2 t - t / 11 15 19 22 7 18 2 3 4 5 + 10 t - 13 t + 2 t + 3 t + 2 t - 3 t - t + 2 t - 4 t + 6 t 13 8 23 20 27 24 10 9 14 - 11 t - 7 t - 2 t + 3 t + t - 2 t - 5 t + 8 t + 6 t 25 26 17 12 + 2 t - t + 4 t + 9 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 117, 228, 428, 802, 1497, 2786, 5253, 9916, 18699, 35288, 66464, 125139, 235868, 444645, 838073, 1579678, 2976519, 5607670, 10566781, 19912067, 37523496, 70714510, 133255982, 251104611] the asympt. constant is, 1.884421158 The low champion is, [1, 0, 1, 0, 0], with asympt. constant, 1.846577102 The high champion is, [0, 0, 0, 0, 0], with asympt. constant, 1.947153929 For words avoiding the pattern, [0, 1, 1, 1, 0], with spacings <=, 2 12 98 38 37 the generating function is, - (1 + 79 t + 34 t - 211 t + 652 t 36 39 14 27 110 112 4 5 + 705 t + 354 t - 20 t - 36 t + 10 t + t + t + t 51 119 24 15 115 113 114 - 1387 t - 3 t - 243 t - 23 t + 11 t + 23 t - 11 t 111 116 13 31 7 11 22 120 + 5 t + t - 32 t + 150 t + 4 t + 28 t - 294 t + t 43 46 45 44 47 50 49 + 95 t - 241 t - 601 t - 204 t - 619 t - 987 t + 174 t 107 76 75 74 77 89 29 - 78 t + 46 t - 1312 t - 34 t - 1072 t - 568 t - 267 t 35 78 65 66 30 69 42 + 250 t + 1683 t + 1295 t - 29 t - 143 t + 1651 t + 330 t 41 105 103 104 106 88 87 + 635 t - 76 t - 78 t - 58 t + 79 t + 168 t - 92 t 90 26 102 81 84 83 82 - 603 t - 123 t - 33 t + 852 t + 929 t - 595 t + 732 t 73 70 72 71 93 92 91 + 340 t + 2136 t + 868 t + 148 t - 236 t - 337 t + 271 t 79 20 18 16 17 85 48 + 479 t - 205 t + 103 t + 4 t + 70 t - 543 t - 209 t 94 97 96 95 101 100 99 - 65 t + 198 t - 381 t + 750 t - 119 t - 166 t + 37 t 19 21 28 32 40 80 86 - 36 t - 195 t - 82 t + 707 t + 990 t + 1006 t - 51 t 109 108 68 67 10 8 25 - 16 t + 29 t - 1485 t + 411 t + 16 t + 11 t - 54 t 23 33 34 54 55 56 58 - 268 t + 926 t + 960 t - 1727 t - 2051 t - 463 t - 1421 t 57 59 63 64 52 53 61 - 1309 t - 1828 t + 2505 t + 1048 t - 1755 t - 570 t + 245 t 62 60 / 12 98 38 37 + 1517 t + 630 t ) / (-1 - 23 t + 87 t + 2 t + 480 t + 10 t / 36 39 14 27 110 112 4 51 - 538 t - 435 t - 16 t - 65 t - 26 t + 4 t - t - 76 t 119 24 15 115 113 114 111 + 3 t - 102 t - 17 t - 22 t - 22 t + 34 t + 5 t 116 121 13 31 7 11 22 120 + 10 t + t + 83 t - 279 t - 4 t + 4 t - 35 t - 4 t 43 46 45 44 47 50 49 - 296 t - 226 t + 326 t - 46 t + 276 t + 493 t - 88 t 107 76 75 74 77 89 29 + 160 t - 1286 t + 1237 t - 19 t + 1346 t + 530 t + 99 t 117 35 78 65 66 6 30 + t + 741 t - 2307 t - 962 t + 1081 t + 2 t + 48 t 69 42 41 105 103 104 106 - 2433 t + 866 t + 417 t + 31 t + 22 t - 7 t - 155 t 88 87 90 26 102 81 84 - 80 t - 97 t - 68 t + 119 t - 54 t - 88 t - 1120 t 83 82 73 70 72 71 93 + 1076 t - 110 t - 180 t - 137 t - 176 t + 2044 t - 113 t 92 91 79 20 18 16 17 + 597 t - 726 t + 998 t + 93 t - 18 t - 5 t - 49 t 85 48 94 97 96 95 101 + 1269 t - 356 t - 96 t - 573 t + 1120 t - 790 t - 79 t 100 99 19 21 28 32 40 + 171 t + 15 t + 73 t - 18 t + 98 t - 379 t - 326 t 80 86 109 108 68 67 9 + 22 t - 429 t + 46 t - 111 t + 2033 t - 735 t + 10 t 10 8 25 23 33 34 54 55 - 16 t - 3 t - 122 t - 34 t + 163 t + 4 t + 1838 t + 25 t 56 58 57 59 63 64 52 - 1274 t + 15 t + 676 t + 182 t - 14 t + 903 t - 445 t 53 61 62 60 - 1366 t + 492 t - 710 t - 1900 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 421, 790, 1478, 2760, 5051, 9240, 16844, 30673, 55882, 101620, 184393, 334412, 606844, 1100281, 1995755, 3620162, 6569165, 11920687, 21634618, 39263063, 71256314, 129338252] the asympt. constant is, 1.815353810 For words avoiding the pattern, [0, 0, 0, 0, 0], with spacings <=, 2 12 38 37 36 the generating function is, - (-1 - 192 t - t + 308 t + 279 t + 23 t 39 14 27 2 3 4 5 51 - 51 t - 205 t + 273 t - 2 t - 4 t - 6 t - 7 t - 17 t 24 15 13 31 7 11 22 - 212 t - 23 t - 183 t + 484 t - 21 t - 110 t + 89 t 43 46 45 44 47 50 49 + 349 t + 129 t + 384 t + 174 t + 251 t - 217 t - 130 t 76 75 77 29 35 78 65 66 + 16 t + 7 t + 18 t + 408 t - 121 t + 13 t - 86 t - 73 t 6 30 69 42 41 26 81 84 - 16 t - 64 t + 30 t - 310 t - 588 t - 92 t - 3 t + 3 t 83 82 70 72 71 79 20 18 + 4 t + 2 t + 17 t + 8 t + 5 t + t + 458 t + 139 t 16 17 85 48 19 21 28 32 - 66 t + 103 t + t - 212 t + 364 t + 320 t + 205 t + 446 t 40 80 68 67 9 10 8 25 - 581 t - 4 t + 61 t + 39 t - 54 t - 67 t - 32 t - 220 t 23 33 34 54 55 56 58 57 - 189 t + 606 t + 84 t - 193 t + 8 t - 68 t - 32 t - 47 t 59 63 64 52 53 61 62 60 + 55 t + 66 t - 49 t - 274 t - 180 t - 44 t - 6 t - 33 t ) / 12 38 37 36 39 14 27 / (1 - 9 t - t + 5 t - 93 t - 48 t + 168 t - 53 t - 94 t / 4 5 51 24 15 13 31 7 - 2 t - 4 t - 154 t - 65 t - 140 t - 49 t - 132 t - 10 t 11 22 43 46 45 44 47 50 - 18 t + 195 t - 399 t + 240 t + 36 t + 86 t - 91 t - 65 t 49 76 75 74 77 29 35 78 65 - 43 t - t - t + 2 t + 2 t - 39 t + 208 t + 5 t + 33 t 66 6 30 69 42 41 26 84 83 + 7 t + 2 t + 405 t + 31 t - 302 t + 72 t - 101 t + t - t 82 73 70 72 71 79 20 18 - 3 t + 9 t + 17 t - 6 t + 13 t + 9 t + 64 t + 37 t 16 17 85 48 19 21 28 32 + 20 t - 81 t + 2 t + 299 t - 28 t + 153 t - 8 t + 127 t 40 80 86 68 67 10 8 25 + 139 t + 4 t + t - 9 t - 89 t - 31 t - 8 t - 25 t 23 33 34 54 55 56 58 57 + 182 t - 57 t + 428 t - 21 t - 152 t - 23 t + 3 t + t 59 63 64 52 53 61 62 60 - 87 t - 64 t + 25 t + 97 t - 101 t + 50 t - 25 t + 34 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 61, 120, 236, 456, 880, 1716, 3345, 6389, 12221, 23367, 45132, 87109, 168035, 324143, 624862, 1205691, 2325603, 4484443, 8645833, 16666427, 32137900, 61969753, 119477120, 230351646, 444110371] the asympt. constant is, 1.928117601 For words avoiding the pattern, [1, 0, 0, 0, 0], with spacings <=, 2 12 38 37 36 39 14 the generating function is, - (1 + t + 19 t + 6 t + t - 3 t + t 27 3 51 24 15 13 31 7 11 + 4 t + t + 3 t - 31 t - 61 t - 10 t - 41 t + 3 t + 21 t 22 43 46 45 44 47 50 49 - 37 t + 31 t + 17 t + 5 t + 18 t + 14 t - 2 t - 6 t 29 35 65 6 30 42 41 26 20 - 21 t + 2 t + t + t - 25 t + 8 t + 11 t - 38 t - 21 t 18 16 17 48 19 21 28 32 - 48 t - 40 t - 42 t + 4 t - 16 t - 19 t - 11 t - 18 t 40 68 67 9 10 8 25 23 33 + 22 t + t - t + t + 13 t + 2 t - 9 t - 29 t - 25 t 34 54 55 56 58 57 59 63 52 - 17 t + 4 t - 5 t - 2 t - 2 t + t + 6 t + 2 t - 9 t 53 61 62 60 / 12 38 37 + t + 4 t + 6 t + 3 t ) / (-1 + 35 t + 2 t + 104 t - 118 t / 36 39 14 27 3 4 5 51 24 - 90 t + 95 t - 7 t - 165 t - t + 2 t - t - 19 t + 9 t 15 13 31 7 11 22 43 46 45 + 72 t - 67 t + 28 t - t + 4 t + 3 t - 77 t - 26 t + 68 t 44 47 50 49 74 29 35 65 - 38 t - 101 t - 68 t + 37 t + t - 74 t + 185 t + 19 t 66 6 30 69 42 41 26 73 70 - t - t - 186 t - 2 t + 121 t + 114 t - 55 t - 3 t - 5 t 72 71 20 18 16 17 48 19 + 2 t + 3 t - 57 t + 94 t - 90 t + 30 t + 77 t + 23 t 21 28 32 40 68 67 9 10 + 71 t + 225 t + 99 t - 200 t + 7 t - 12 t - 5 t - 8 t 8 25 23 33 34 54 55 56 + 3 t + 142 t - 133 t - 98 t + 5 t - 32 t + 45 t - 3 t 58 57 59 63 64 52 53 61 + 18 t - 11 t + 20 t - 5 t - 16 t + 92 t - 66 t + t 62 60 + 14 t - 27 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 424, 804, 1522, 2881, 5364, 9979, 18542, 34478, 64015, 118876, 220754, 409885, 760464, 1410662, 2616797, 4854417, 9002623, 16694937, 30960105, 57414373, 106468951, 197434202] the asympt. constant is, 1.854320341 For words avoiding the pattern, [0, 1, 0, 0, 0], with spacings <=, 2 12 38 37 36 the generating function is, - (1 + 77 t + 310 t - 363 t + 719 t 39 14 27 81 84 83 82 87 + 406 t - 101 t - 107 t + 32 t + 28 t - 69 t - 88 t - 8 t 80 4 51 24 15 86 79 85 + 3 t + t + 281 t - 157 t - 55 t - 42 t - 172 t + 14 t 13 31 7 11 22 43 46 45 - 75 t - 835 t + 2 t + 14 t + 131 t + 257 t - 452 t + 89 t 44 47 50 49 78 74 88 - 533 t - 237 t - 176 t + 204 t - 70 t + 158 t + 22 t 29 35 65 66 30 69 42 + 34 t - 366 t + 98 t - 246 t - 209 t + 301 t + 389 t 41 26 73 70 72 71 20 18 - 154 t + 260 t + 299 t + 74 t + 23 t - 30 t + 39 t - 50 t 16 17 48 19 21 28 32 - 95 t - 106 t - 448 t + 179 t + 209 t - 6 t - 146 t 40 68 67 9 10 8 25 23 + 232 t - 36 t + 58 t - 4 t - t + 9 t + 438 t + 262 t 33 34 54 55 56 58 57 - 701 t - 73 t + 204 t + 712 t + 454 t + 386 t - 119 t 59 63 64 52 53 89 92 91 - 127 t - 747 t - 406 t + 861 t + 470 t + 6 t + 8 t + 10 t 90 95 61 62 60 96 77 76 - 2 t + 2 t - 70 t - 565 t - 724 t + 2 t + 139 t + 55 t 75 / 12 38 37 36 39 + 21 t ) / (-1 - 47 t + 2 t - 509 t + 993 t - 1060 t + 316 t / 14 27 81 84 83 82 87 80 + 5 t + 187 t - 60 t - 93 t - 8 t + 117 t - 32 t - 160 t 4 5 51 24 15 86 79 85 - t + t - 468 t + 387 t - 49 t + 62 t + 106 t + 6 t 13 31 7 11 22 43 46 45 + 102 t + 482 t - 2 t - 9 t + 114 t - 34 t + 427 t - 364 t 44 47 50 49 78 74 88 + 456 t - 438 t + 322 t - 446 t + 168 t + 114 t - 30 t 29 35 65 66 30 69 42 - 214 t + 546 t - 407 t + 280 t + 79 t - 273 t - 350 t 41 26 73 70 72 71 20 + 542 t + 139 t - 269 t + 165 t - 14 t + 113 t + 147 t 18 16 17 97 48 19 21 28 - 40 t + 3 t + 24 t + 2 t + 274 t - 142 t - 84 t + 46 t 32 40 68 67 9 10 8 25 - 608 t - 278 t + 194 t - 218 t + 12 t - 6 t - 5 t - 461 t 23 33 34 54 55 56 58 - 126 t + 348 t - 607 t + 184 t - 311 t + 169 t - 539 t 57 59 63 64 52 53 89 + 605 t + 265 t + 97 t - 257 t - 262 t + 510 t + 16 t 92 91 90 95 61 62 60 93 + 2 t - 12 t + 10 t - 2 t - 527 t + 207 t + 441 t + 8 t 77 76 75 - 105 t + 5 t + 130 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 423, 798, 1509, 2852, 5271, 9759, 18107, 33552, 62369, 115930, 215401, 400135, 744183, 1383244, 2570284, 4776532, 8880929, 16510957, 30693664, 57062814, 106068984, 197167766] the asympt. constant is, 1.858901052 For words avoiding the pattern, [1, 1, 0, 0, 0], with spacings <=, 2 12 38 37 36 39 the generating function is, - (1 + 3 t - 97 t - 173 t - 77 t + 43 t 14 27 81 84 83 82 80 5 51 + 2 t + 135 t + 13 t + t - t + 8 t + 11 t + t + 59 t 24 15 79 85 13 31 7 11 + 164 t + 17 t + t - 3 t - 25 t + 60 t + 7 t + 36 t 22 43 46 45 44 47 50 - 20 t + 286 t + 103 t - 273 t - 187 t - 176 t + 305 t 49 78 74 88 29 35 65 66 + 248 t - 8 t + 25 t - 4 t - 346 t - 238 t + 56 t + 97 t 30 69 42 41 26 73 70 72 + 78 t + 75 t - 197 t - 209 t - 63 t - 37 t - 67 t - t 71 20 18 16 17 48 19 21 - 21 t - 74 t + 96 t + 28 t + 74 t - 218 t - 22 t - 3 t 28 32 40 68 67 10 8 25 - 61 t + 33 t + 173 t + 46 t - 29 t + 14 t + 6 t + 167 t 23 33 34 54 55 56 58 - 48 t + 361 t - 13 t - 358 t - 189 t + 240 t + 62 t 57 59 63 64 52 53 89 92 + 162 t + 216 t + 45 t - 24 t - 19 t - 95 t + t + t 61 62 60 77 76 75 / 12 - 240 t + 6 t - 61 t - 26 t - 19 t + 22 t ) / (-1 + 66 t / 38 37 36 39 14 27 98 + 2 t - 703 t + 527 t - 421 t - 373 t - 26 t - 987 t - 5 t 81 84 83 82 87 80 5 51 - 147 t + 212 t + 155 t - 91 t - 7 t - 196 t - 2 t + 153 t 24 15 86 79 85 13 31 7 - 414 t + 101 t + 21 t - 313 t + 98 t - 85 t + 1742 t - 7 t 11 22 43 46 45 44 47 - 8 t + 323 t - 956 t + 569 t - 1788 t + 1455 t + 2279 t 50 49 78 74 88 29 94 + 1474 t - 57 t + 136 t - 285 t - 103 t - 199 t + 14 t 35 65 66 30 69 42 41 - 1151 t - 101 t + 743 t - 682 t + 1407 t - 1406 t + 474 t 26 73 70 72 71 20 18 + 195 t - 725 t - 259 t + 256 t - 611 t - 90 t - 17 t 16 17 97 48 19 21 28 - 82 t + 41 t - 6 t - 1716 t + 24 t - 95 t + 1062 t 32 40 68 67 9 10 8 6 - 450 t - 357 t + 237 t - 270 t + 2 t - 15 t + 8 t + 2 t 25 23 33 34 54 55 56 + 686 t + 56 t - 578 t + 939 t + 91 t - 1233 t + 132 t 58 57 59 63 64 52 53 - 1260 t - 685 t + 1118 t - 146 t - 1288 t + 779 t + 1355 t 89 92 91 90 95 102 61 62 - 59 t + 49 t - 26 t - 41 t + 24 t + t - 805 t + 111 t 60 93 96 103 77 99 76 75 + 697 t + 23 t - 4 t + 2 t + 387 t - 8 t + 176 t + 460 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 422, 793, 1486, 2780, 5074, 9248, 16895, 30746, 55790, 101040, 182466, 329388, 593508, 1067591, 1919448, 3450200, 6192291, 11107885, 19921326, 35705905, 63972790, 114586333] the asympt. constant is, 1.787461079 For words avoiding the pattern, [1, 0, 1, 0, 0], with spacings <=, 2 12 38 37 36 39 the generating function is, (1 + 5 t + 30 t + 102 t + 270 t - 245 t 14 27 98 81 84 83 82 87 - 73 t + 211 t - 3 t - 39 t + 3 t - 74 t - 61 t + 8 t 100 80 5 51 24 15 86 79 - 4 t + 54 t + t + 265 t - 88 t - 74 t + 48 t + 5 t 85 13 31 7 11 22 43 46 + 55 t - 58 t + 54 t + 6 t + 21 t + 22 t - 527 t + 248 t 45 44 47 50 49 78 74 + 49 t - 211 t - 75 t + 313 t - 254 t + 39 t - 332 t 88 29 94 35 65 66 30 - 24 t - 275 t + 15 t - 167 t + 177 t + 72 t - 206 t 69 42 41 26 73 70 72 - 67 t - 340 t - 81 t + 121 t - 359 t + 177 t + 129 t 71 20 18 16 17 97 48 19 + 446 t + 11 t + 50 t - 24 t + 31 t + 4 t - 313 t + 53 t 21 28 32 40 68 67 9 10 + 37 t - 147 t + 236 t + 51 t - 39 t + 150 t - 4 t + 7 t 8 25 23 33 34 54 55 56 + 2 t + 60 t - 27 t + 154 t + 101 t + 407 t + 42 t - 421 t 58 57 59 63 64 52 53 - 288 t - 444 t + 109 t + 188 t - 67 t + 520 t + 337 t 89 92 91 90 95 102 61 62 + 3 t - 19 t - 10 t - 3 t + 6 t + 2 t - 48 t - 418 t 60 93 96 77 99 101 76 75 + 2 t + 7 t + 2 t + 83 t - 9 t + 2 t + 201 t - 128 t ) / 12 38 37 36 39 14 / (1 - 41 t - 2 t + 345 t + 712 t - 1177 t - 515 t + 33 t / 116 115 27 98 81 84 83 82 + t - t + 464 t + 49 t - 490 t + 253 t + 45 t - 649 t 87 107 100 113 106 112 105 + 405 t - 8 t - 162 t + 4 t - 20 t + 13 t - 8 t 80 5 51 24 15 86 79 85 - 84 t + 2 t - 431 t + 422 t - 49 t + 164 t - 140 t - 132 t 13 31 7 11 22 43 46 45 + 60 t + 368 t + 6 t - t + 27 t + 593 t + 947 t + 871 t 44 47 50 49 78 74 88 + 2078 t - 574 t - 1016 t - 1652 t + 569 t - 1555 t + 575 t 29 94 35 65 66 30 69 + 141 t + 136 t - 199 t + 1160 t - 1402 t + 205 t + 1548 t 42 41 26 73 70 72 71 + 57 t + 323 t - 188 t + 67 t + 1191 t - 449 t + 242 t 20 18 17 97 48 19 21 + 101 t - 41 t - 63 t + 10 t + 1105 t - 154 t - 21 t 28 32 40 68 67 104 9 10 + 132 t - 781 t - 957 t - 419 t + 94 t + 16 t + 8 t + 11 t 8 6 25 23 33 34 54 55 - 10 t - 2 t - 307 t + 63 t - 22 t - 701 t + 347 t - 1638 t 56 58 57 59 63 64 52 - 430 t - 82 t - 2794 t + 436 t + 45 t - 1077 t + 2413 t 53 89 92 91 90 95 102 - 1561 t + 81 t - 167 t - 176 t - 167 t + 119 t + 45 t 61 62 60 93 96 103 77 + 1347 t + 1319 t + 1106 t - 54 t + 13 t + 67 t + 564 t 99 101 111 110 109 114 76 75 - 59 t - 57 t + 3 t - 9 t - 6 t - 4 t - 21 t - 861 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 416, 774, 1442, 2686, 4858, 8758, 15808, 28585, 51527, 92803, 167024, 300675, 539788, 967996, 1735771, 3112642, 5575350, 9983281, 17875636, 32008911, 57303218, 102569965] the asympt. constant is, 1.789008377 For words avoiding the pattern, [0, 1, 1, 0, 0], with spacings <=, 2 12 38 37 36 the generating function is, - (1 + 87 t - 603 t + 231 t + 4415 t 39 14 27 98 81 84 83 - 2850 t + 8 t + 713 t + 26 t + 232 t + 225 t - 109 t 82 87 107 100 106 105 80 4 - 419 t - 409 t - 5 t + 26 t + 3 t - 8 t + 51 t + t 5 51 24 15 86 79 85 13 + t + 1704 t - 1187 t - 14 t - 150 t + 1078 t - 2 t - 69 t 31 7 11 22 43 46 45 - 1477 t + 7 t + 21 t - 163 t + 3260 t - 2104 t - 1583 t 44 47 50 49 78 74 88 + 1729 t - 2429 t + 1877 t - 364 t - 353 t - 1297 t - 70 t 29 108 94 35 65 66 30 + 1442 t + 5 t - 14 t + 588 t + 2538 t + 213 t + 671 t 69 42 41 26 73 70 72 + 964 t + 860 t - 2990 t + 55 t + 842 t - 1610 t + 663 t 71 20 18 16 17 97 48 + 1144 t - 55 t - 169 t - 28 t - 195 t - 26 t - 5539 t 19 21 28 32 40 68 67 + 238 t + 46 t + 369 t - 589 t - 1079 t - 443 t + 1742 t 104 10 8 25 23 33 34 54 + 15 t + 8 t + 15 t - 41 t - 91 t + 28 t + 1479 t - 2890 t 55 56 58 57 59 63 64 - 2282 t - 910 t - 1268 t + 1702 t + 2978 t + 1981 t - 546 t 52 53 89 92 91 90 95 + 790 t + 1276 t - 264 t + 104 t - 33 t - 150 t - 58 t 102 61 62 60 93 96 103 + 16 t - 501 t - 2365 t + 272 t + 34 t + 34 t - 18 t 77 99 101 111 110 76 75 / + 514 t - 55 t - 32 t + 2 t + 2 t - 485 t + 639 t ) / ( / 12 38 37 36 39 14 -1 - 41 t + 2 t + 596 t + 2939 t - 2616 t + 1916 t - 69 t 27 98 81 84 83 82 87 - 417 t - 36 t - 463 t - 182 t - 433 t + 754 t + 287 t 107 100 106 112 105 80 4 51 + 8 t - 82 t - 11 t + 2 t + 24 t + 803 t - t - 962 t 24 15 86 79 85 13 31 + 797 t + 30 t + 153 t - 1124 t + 88 t + 103 t + 1487 t 7 11 22 43 46 45 44 - 7 t - 5 t + 152 t - 1614 t + 1363 t + 2242 t + 1036 t 47 50 49 78 74 88 29 - 946 t - 731 t - 4505 t + 484 t + 2096 t - 439 t - 955 t 108 94 35 65 66 30 69 - 9 t + 37 t + 1289 t - 2131 t + 1626 t + 749 t - 1536 t 42 41 26 73 70 72 71 - 2700 t + 1615 t - 127 t + 152 t + 2656 t - 124 t - 2289 t 20 18 16 17 97 48 19 + 212 t - 99 t - 25 t + 150 t + 48 t + 2170 t - 238 t 21 28 32 40 68 67 104 - 111 t + 698 t - 685 t - 2645 t + 1683 t - 1094 t - 32 t 9 10 8 6 25 23 33 34 + 16 t - 8 t - t + 2 t - 909 t - 105 t - 627 t - 1169 t 54 55 56 58 57 59 + 4453 t - 441 t - 1434 t + 2987 t - 2613 t - 3620 t 63 64 52 53 89 92 91 - 3873 t + 2320 t + 1372 t - 823 t + 291 t - 151 t - 63 t 90 95 102 61 62 60 93 - 187 t + 20 t - 48 t + 2035 t + 2363 t + 732 t + 41 t 96 103 77 99 101 110 109 - 50 t + 31 t - 431 t + 77 t + 53 t - 2 t + 5 t 76 75 + 836 t - 1625 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 224, 419, 782, 1454, 2703, 4892, 8887, 16068, 28960, 52249, 94190, 169728, 305875, 552171, 995483, 1795813, 3239505, 5849665, 10559582, 19071106, 34443752, 62210474, 112372649] the asympt. constant is, 1.806240440 For words avoiding the pattern, [0, 0, 1, 0, 0], with spacings <=, 2 12 38 37 36 the generating function is, - (-1 - 106 t - 461 t - 767 t - 1795 t 39 14 27 98 81 84 83 + 439 t + 35 t + 633 t - 10 t + 540 t + 266 t + 36 t 82 87 100 3 80 4 51 24 + 50 t + 168 t - 5 t - t + 325 t - t + 651 t + 892 t 15 86 79 85 13 31 7 11 - 72 t - 321 t - 85 t - 219 t + 58 t - 2896 t - 4 t - 13 t 22 43 46 45 44 47 50 + 282 t + 554 t - 467 t - 1749 t - 1868 t - 1743 t + 2403 t 49 78 74 88 29 94 35 + 2370 t + 432 t + 998 t + 141 t - 1763 t - 4 t - 3987 t 65 66 30 69 42 41 26 + 2023 t + 2463 t - 1215 t - 606 t + 1359 t - 1040 t + 730 t 73 70 72 71 20 18 16 - 331 t + 211 t - 631 t + 370 t + 430 t + 152 t + 60 t 17 97 48 19 21 28 32 + 80 t - 4 t - 1787 t + 282 t + 877 t - 902 t - 3915 t 40 68 67 104 9 10 8 6 + 707 t + 801 t + 1370 t + t - 24 t - 10 t - 9 t - 5 t 25 23 33 34 54 55 56 + 360 t + 591 t - 2057 t - 3439 t + 1622 t + 696 t + 716 t 58 57 59 63 64 52 53 - 1693 t - 1730 t + 124 t + 1152 t + 483 t + 2090 t + 2423 t 89 92 91 90 95 102 61 - 174 t + 41 t + 152 t - 58 t + 20 t - 7 t - 170 t 62 60 93 96 103 77 99 101 + 1403 t - 673 t - 61 t + t - 2 t + 209 t - 15 t - 3 t 76 75 / 12 38 37 36 - 757 t + 136 t ) / (1 + 84 t - 2 t - 517 t - 395 t - 3111 t / 39 14 27 81 84 83 82 - 1239 t + 16 t - 323 t - 524 t - 698 t + 140 t + 984 t 87 100 105 3 80 4 5 51 24 - 563 t - 15 t + t + t - 449 t - t - t + 2350 t - 447 t 15 86 79 85 13 31 7 + 138 t + 396 t + 1034 t + 464 t - 133 t + 1071 t - 6 t 11 22 43 46 45 44 47 - 2 t + 660 t + 862 t - 1621 t - 1723 t + 2292 t + 2467 t 50 49 78 74 88 29 94 + 1733 t - 3715 t - 326 t - 1676 t - 135 t + 369 t - 44 t 35 65 66 30 69 42 41 + 169 t + 476 t - 486 t - 1669 t + 1704 t - 2063 t + 1705 t 26 73 70 72 71 20 18 - 367 t - 86 t - 1464 t + 1676 t - 635 t - 14 t - 7 t 16 17 97 48 19 21 28 - 192 t + 40 t - 5 t - 949 t + 73 t - 146 t + 1423 t 32 40 68 67 104 9 10 8 + 109 t - 119 t + 1365 t + 354 t - 3 t + 18 t - 43 t + t 6 25 23 33 34 54 55 + 5 t + 1384 t - 110 t - 2665 t - 334 t + 3147 t - 505 t 56 58 57 59 63 64 52 - 1178 t + 178 t + 2977 t - 3166 t - 304 t + 1569 t - 2618 t 53 89 92 91 90 95 102 + 902 t + 378 t + 66 t - 221 t - 30 t - 31 t + 5 t 61 62 60 93 96 103 77 + 1650 t - 2315 t + 642 t + 114 t + 26 t - 5 t - 1122 t 99 101 76 75 + 10 t - 5 t + 1079 t + 904 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 225, 425, 806, 1525, 2890, 5344, 9930, 18457, 34346, 63948, 119130, 222180, 414305, 773354, 1446243, 2703266, 5052570, 9447729, 17662086, 33015343, 61708074, 115332993, 215539751] the asympt. constant is, 1.868570866 For words avoiding the pattern, [1, 0, 0, 1, 0], with spacings <=, 2 12 38 37 36 the generating function is, (-1 - 26 t + 870 t + 1140 t - 2660 t 39 14 27 81 84 83 82 - 397 t + 48 t + 29 t - 192 t + 194 t + 47 t - 475 t 87 3 80 5 51 24 15 86 - 69 t - t - 719 t - t - 1007 t + 385 t + 24 t + 103 t 79 85 13 31 7 11 22 43 + 439 t + 189 t + 36 t - 92 t - 4 t - 39 t - 61 t - 3542 t 46 45 44 47 50 49 78 + 3665 t + 1564 t - 1452 t + 6291 t - 1012 t - 142 t + 287 t 74 88 29 35 65 66 30 + 358 t - 35 t - 1203 t - 1554 t + 831 t + 2183 t - 867 t 69 42 41 26 73 70 72 + 3526 t - 5190 t - 1910 t - 166 t - 308 t + 2799 t + 1695 t 71 20 18 16 17 48 19 + 865 t + 345 t + 175 t + 110 t + 52 t + 6342 t + 272 t 21 28 32 40 68 67 9 + 542 t - 1206 t - 16 t - 241 t + 3866 t + 1741 t - 28 t 10 8 6 25 23 33 34 54 - 17 t - 6 t - 5 t - 621 t + 41 t - 988 t + 724 t + 6104 t 55 56 58 57 59 63 + 5551 t + 1581 t - 798 t + 1500 t - 1273 t + 1898 t 64 52 53 89 92 91 90 + 1765 t + 174 t + 2556 t - 72 t + 2 t - 5 t - 6 t 61 62 60 77 76 75 / + 1287 t + 764 t - 1176 t + 1251 t + 484 t + 839 t ) / (-1 / 12 38 37 36 39 14 + 46 t + 2 t + 563 t - 2475 t + 707 t - 1447 t - 16 t 27 81 84 83 82 87 3 80 - 150 t + 346 t - 15 t + 108 t + 143 t - 73 t - t - 845 t 4 5 51 24 15 86 79 85 + 2 t - 2 t + 3844 t - 85 t - 29 t + 7 t - 114 t - 3 t 13 31 7 11 22 43 46 - 82 t + 612 t + 6 t - 5 t - 148 t + 1855 t - 5328 t 45 44 47 50 49 78 74 + 4402 t - 1241 t + 289 t + 275 t + 5675 t - 409 t + 775 t 88 29 35 65 66 30 69 + 33 t + 116 t - 441 t + 4933 t - 757 t - 627 t + 1009 t 42 41 26 73 70 72 71 - 67 t + 1797 t - 242 t - 1703 t - 394 t + 1049 t - 3181 t 20 18 16 17 48 19 21 - 131 t + 236 t - 2 t + 38 t - 3398 t - 368 t + 217 t 28 32 40 68 67 9 10 8 + 818 t - 69 t - 710 t + 321 t + 4822 t - 27 t + 39 t + 2 t 6 25 23 33 34 54 55 - 3 t + 475 t + 351 t - 1838 t + 1014 t + 2438 t - 6279 t 56 58 57 59 63 64 52 + 1816 t + 8030 t - 4270 t + 62 t - 511 t - 5211 t + 2794 t 53 89 92 91 90 61 62 60 - 6771 t + 2 t + 4 t - 4 t + 3 t - 688 t - 5267 t + 4354 t 77 76 75 - 48 t + 914 t + 758 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 116, 225, 425, 802, 1514, 2861, 5228, 9540, 17414, 31787, 57889, 105672, 193035, 352655, 642964, 1176306, 2152438, 3939077, 7198325, 13157366, 24043123, 43930771, 80251374, 146656978] the asympt. constant is, 1.827138887 For words avoiding the pattern, [0, 1, 0, 1, 0], with spacings <=, 2 12 38 37 36 the generating function is, - (1 + 116 t + 2132 t + 566 t - 2355 t 39 14 95 27 81 84 83 + 3256 t + 135 t - 336 t + 979 t - 2787 t - 1157 t - 1911 t 82 87 114 120 2 80 4 5 51 - 906 t + 1059 t - 7 t + t + t - 1253 t + 4 t + t + 167 t 119 24 104 15 86 79 85 13 - t + 10 t + 10 t - 84 t - 405 t - 1084 t + 159 t + 29 t 31 7 11 93 22 43 46 + 125 t + 7 t + 33 t - 512 t - 803 t + 204 t - 1342 t 45 44 47 50 49 78 74 - 4262 t + 7210 t - 3935 t - 3638 t - 949 t + 494 t + 2310 t 88 29 94 35 65 66 30 + 430 t + 735 t + 158 t + 82 t + 6555 t + 3377 t + 195 t 69 42 41 123 121 122 26 - 1292 t + 10424 t + 4064 t + t + 2 t + t + 954 t 109 73 70 72 71 20 18 - 20 t + 5051 t - 2398 t - 1642 t + 3462 t - 769 t - 449 t 16 17 48 116 117 118 19 + 24 t - 247 t - 4347 t - 10 t - 11 t - 3 t - 288 t 21 28 32 40 105 106 107 - 387 t + 1604 t - 2005 t + 8973 t + 9 t - 41 t - 30 t 108 110 68 67 9 10 8 6 + 4 t + 31 t + 628 t - 1978 t + 6 t + 47 t + 26 t + 11 t 25 23 33 34 54 55 56 + 278 t - 253 t - 51 t - 4284 t - 1778 t - 3804 t - 8570 t 58 57 59 63 64 52 - 15029 t - 10600 t - 9591 t + 12361 t + 2900 t + 518 t 53 89 92 91 90 103 61 + 854 t - 239 t - 200 t - 877 t + 33 t + 95 t + 3935 t 115 62 60 77 96 112 113 - 23 t - 3438 t - 10469 t + 2901 t + 487 t + 15 t - 20 t 111 102 97 99 100 98 101 - 10 t + 108 t + 31 t + 317 t + 181 t + 387 t + 251 t 76 75 / 12 38 37 + 4183 t + 5164 t ) / (-1 - 51 t + 2 t - 3057 t + 201 t / 36 39 14 95 27 81 84 + 189 t + 3525 t - 61 t + 518 t - 306 t + 946 t - 1094 t 83 82 87 114 120 2 3 80 + 1610 t - 1959 t - 1353 t - 15 t - 2 t - t + 2 t - 271 t 4 5 51 119 24 104 15 86 - 4 t + 6 t - 4734 t - 2 t + 45 t + 46 t + 109 t + 300 t 79 85 13 31 7 11 93 + 1234 t - 840 t + 67 t - 555 t + 15 t + 37 t + 321 t 22 43 46 45 44 47 50 + 292 t + 9089 t - 2178 t + 8186 t - 5310 t + 561 t + 4542 t 49 78 74 88 29 94 35 - 4614 t + 1397 t + 2663 t + 276 t - 5 t - 572 t - 2481 t 65 66 30 69 42 41 121 - 3101 t + 4332 t + 1049 t + 35 t - 5911 t + 7297 t - t 122 26 109 73 70 72 71 + t - 33 t + 35 t - 4984 t + 1148 t + 5658 t - 4231 t 20 18 16 17 48 116 117 118 + 334 t + 139 t - 60 t + 65 t + 1988 t - 12 t + t - 7 t 19 21 28 32 40 105 106 - 276 t - 478 t + 429 t + 1646 t - 5417 t + 17 t + 36 t 107 108 110 68 67 9 10 + 5 t - 40 t - 59 t - 1285 t + 3253 t + 27 t - 35 t 8 6 25 23 33 34 54 - 12 t - 9 t - 341 t - 570 t - 1830 t + 2071 t + 2264 t 55 56 58 57 59 63 - 3763 t + 5490 t + 6622 t - 5012 t - 7680 t - 13615 t 64 52 53 89 92 91 90 + 7968 t + 1710 t - 2868 t + 1034 t - 832 t + 1192 t - 856 t 103 61 115 62 60 77 124 + 32 t - 12974 t + 15 t + 7042 t + 4099 t + 2290 t + t 96 112 113 111 102 97 99 - 825 t - 31 t + 33 t + 42 t + 119 t + 538 t + 76 t 100 98 101 76 75 + 200 t - 312 t - 75 t + 26 t - 1817 t ) the first , 30, terms are , [2, 4, 8, 16, 31, 60, 117, 228, 428, 802, 1497, 2786, 5104, 9336, 17018, 31076, 56945, 104285, 192121, 353999, 653096, 1205125, 2221736, 4096796, 7548507, 13909603, 25625929, 47214107, 86993596, 160280114] the asympt. constant is, 1.842335094 The low champion is, [1, 1, 0, 0, 0], with asympt. constant, 1.787461079 The high champion is, [0, 0, 0, 0, 0], with asympt. constant, 1.928117601 This took, 169.570, seconds