Minimally Complex Sequences

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4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, ...

MCS62064 : A₀ = 1; A_K+1 = A_K + 3 K (score: 4)

4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, ...

MCS213537 (alias MCS1725633) : A₀ = 0; A₁ = 0; A_K+1 = A_K-1 + K² (score: 4)

Tetrahedral numbers (A0292)

4, 10, 22, 46, 94, 190, 382, 766, 1534, 3070, 6142, 12286, 24574, 49150, 98302, 196606, 393214, 786430, 1572862, 3145726, 6291454, 12582910, 25165822, 50331646, 100663294, 201326590, 402653182, ...

MCS125600 : A₀ = 1; A_N = 2 A_N-1 + 2 (score: 4)

4, 10, 25, 61, 148, 358, 865, 2089, 5044, 12178, 29401, 70981, 171364, 413710, 998785, 2411281, 5821348, 14053978, 33929305, 81912589, 197754484, 477421558, 1152597601, 2782616761, 6717831124, ...

MCS6967814 : A₀ = 1; A₁ = 1; A_N = 2 A_N-1 + A_N-2 + 1 (score: 5)

4, 10, 28, 76, 208, 568, 1552, 4240, 11584, 31648, 86464, 236224, 645376, 1763200, 4817152, 13160704, 35955712, 98232832, 268377088, 733219840, 2003193856, 5472827392, 14952042496, 40849739776, ...

MCS3450118 : A₀ = 1; A₁ = 1; A_N = 2 A_N-1 + 2 A_N-2 (score: 5)

Horadam sequence W_n(1, 1; 2, 2)

4, 10, -30, -77, 232, 684, -2330, -7535, 27948, 97942, -391286, -1469145, 6260560, 24975448, -112690098, -474533531, 2253801940, 9965204130, -49583642702, -229199695013, ...

MCS429081 : A₀ = -1; A₁ = 0; A_K+1 = - K A_K-1 - K (score: 5)

4, -10, 35, -166, 960, -6555, 51479, -456757, 4516090, -49220234, 586126717, -7570427088, 105399852514, ...

MCS3509638 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K - A_K-1 - 1 (score: 5)

4, -11, 10, 13, -56, 73, 22, -263, 460, -131, -1118, 2629, -1904, -4079, 13870, -15503, -10604, 67717, -103622, 4093, 302680, -617639, 327238, 1198441, -3378596, 3161869, 3812050, -17109707, ...

MCS53967 : A₀ = 0; A₁ = 1; A_N = - 2 A_N-1 - 3 A_N-2 (score: 6)

(Not in OEIS)

Horadam sequence W_n(0, 1; -3, -2), Lucas sequence U_n(-2, 3)

4, -11, 13, -26, 37, -65, 100, -167, 265, -434, 697, -1133, 1828, -2963, 4789, -7754, 12541, -20297, 32836, -53135, 85969, -139106, 225073, -364181, 589252, -953435, 1542685, -2496122, 4038805, ...

MCS14004742 : A₀ = 1; A₁ = 1; A_N = - A_N-1 + A_N-2 - 2 (score: 5)

4, -11, 18, -41, 76, -159, 310, -629, 1248, -2507, 5002, -10017, 20020, -40055, 80094, -160205, 320392, -640803, 1281586, -2563193, 5126364, -10252751, 20505478, -41010981, 82021936, -164043899, ...

MCS505264 : A₀ = 1; A_K+1 = - 2 A_K - K - 1 (score: 4)

4, 11, 22, 37, 56, 79, 106, 137, 172, 211, 254, 301, 352, 407, 466, 529, 596, 667, 742, 821, 904, 991, 1082, 1177, 1276, 1379, 1486, 1597, 1712, 1831, 1954, 2081, 2212, 2347, 2486, 2629, 2776, ...

MCS28306 : A_K = 2 K² + K + 1 (score: 5)

4, 11, 24, 45, 76, 119, 176, 249, 340, 451, 584, 741, 924, 1135, 1376, 1649, 1956, 2299, 2680, 3101, 3564, 4071, 4624, 5225, 5876, 6579, 7336, 8149, 9020, 9951, 10944, 12001, 13124, 14315, 15576, ...

MCS31304 : A₀ = 0; A_K+1 = A_K + K² + K + 1 (score: 5)

4, 11, 24, 47, 84, 143, 232, 367, 564, 855, 1272, 1879, 2740, 3983, 5736, 8255, 11796, 16871, 23992, 34183, 48468, 68895, 97512, 138415, 195700, 277559, 392184, 555959, 785268, 1112879, 1571560, ...

MCS427297 : A₀ = 0; A₁ = 0; A_K+1 = 2 A_K-1 + K² (score: 5)

4, -11, 25, -62, 148, -359, 865, -2090, 5044, -12179, 29401, -70982, 171364, -413711, 998785, -2411282, 5821348, -14053979, 33929305, -81912590, 197754484, -477421559, 1152597601, -2782616762, ...

MCS14070278 : A₀ = 1; A₁ = 1; A_N = - 2 A_N-1 + A_N-2 - 1 (score: 5)

4, 11, 26, 57, 120, 247, 502, 1013, 2036, 4083, 8178, 16369, 32752, 65519, 131054, 262125, 524268, 1048555, 2097130, 4194281, 8388584, 16777191, 33554406, 67108837, 134217700, 268435427, ...

MCS970 (alias MCS3914, MCS502432) : A₀ = 0; A_K+1 = 2 A_K + K (score: 3)

2^X-X-1 (Eulerian numbers) (A0295)

4, 11, 29, 73, 180, 439, 1065, 2577, 6228, 15043, 36325, 87705, 211748, 511215, 1234193, 2979617, 7193444, 17366523, 41926509, 101219561, 244365652, 589950887, 1424267449, 3438485809, 8301239092, ...

MCS6902278 : A₀ = 1; A₁ = 1; A_K+1 = 2 A_K + A_K-1 + K (score: 5)

4, -11, 34, -101, 304, -911, 2734, -8201, 24604, -73811, 221434, -664301, 1992904, -5978711, 17936134, -53808401, 161425204, -484275611, 1452826834, -4358480501, 13075441504, -39226324511, ...

MCS501697 : A₀ = -1; A_N = - 3 A_N-1 + 1 (score: 5)

4, -11, 38, -131, 490, -1897, 7714, -32501, 142142, -641795, 2989294, -14321923, 70493962, -355816769, 1839536930, -9727958933, 52567582606, -289966384939, ...

MCS3452966 : A₀ = 1; A₁ = 1; A_K+1 = - 2 A_K + K A_K-1 (score: 5)

4, -11, 46, -227, 1366, -9557, 76462, -688151, 6881518, -75696689, 908360278, -11808683603, 165321570454, ...

MCS505496 : A₀ = 1; A_K+1 = - K A_K - A_K + K - 1 (score: 5)

4, 12, 24, 37, 49, 61, 76, 96, 120, 145, 169, 193, 220, 252, 288, 325, 361, 397, 436, 480, 528, 577, 625, 673, 724, 780, 840, 901, 961, 1021, 1084, 1152, 1224, 1297, 1369, 1441, 1516, 1596, 1680, ...

MCS3443846 : A₀ = 1; A₁ = 1; A_K+1 = A_K - A_K-1 + K² (score: 5)

4, 12, 24, 40, 60, 84, 112, 144, 180, 220, 264, 312, 364, 420, 480, 544, 612, 684, 760, 840, 924, 1012, 1104, 1200, 1300, 1404, 1512, 1624, 1740, 1860, 1984, 2112, 2244, 2380, 2520, 2664, 2812, ...

MCS7755 (alias MCS14122, MCS28250) : A₀ = 0; A_K+1 = A_K + 4 K (score: 5)

4, 12, 27, 51, 86, 134, 197, 277, 376, 496, 639, 807, 1002, 1226, 1481, 1769, 2092, 2452, 2851, 3291, 3774, 4302, 4877, 5501, 6176, 6904, 7687, 8527, 9426, 10386, 11409, 12497, 13652, 14876, ...

MCS248136 : A₀ = 1; A_K+1 = A_K + K² + 2 K (score: 5)

4, 12, 32, 81, 200, 488, 1184, 2865, 6924, 16724, 40384, 97505, 235408, 568336, 1372096, 3312545, 7997204, 19306972, 46611168, 112529329, 271669848, 655869048, 1583407968, 3822685009, 9228778012, ...

MCS1725569 : A₀ = 0; A₁ = 0; A_K+1 = 2 A_K + A_K-1 + K (score: 5)

4, 12, 32, 85, 228, 644, 1888, 5877, 18980, 64768, 227904, 842153, 3190852, 12632520, 51053888, 214753129, 918970308, 4080309812, 18379406560, 85686506493, 404346944804, ...

MCS213129 : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 + K² (score: 5)

4, 12, 35, 103, 306, 914, 2737, 8205, 24608, 73816, 221439, 664307, 1992910, 5978718, 17936141, 53808409, 161425212, 484275620, 1452826843, 4358480511, 13075441514, 39226324522, 117678973545, ...

MCS250800 : A₀ = 1; A_K+1 = 3 A_K - K + 1 (score: 5)

4, -12, 69, -420, 3016, -24540, 223885, -2263380, 25121076, -303716280, 3973432729, -55931774472, 842950049824, ...

MCS856673 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K + A_K-1 + K (score: 5)

4, -13, 16, -49, 72, -181, 312, -689, 1296, -2693, 5264, -10673, 21176, -42549, 84872, -170001, 339712, -679749, 1359136, -2718673, 5436904, -10874293, 21748056, -43496689, 86992752, -173986181, ...

MCS505228 : A₀ = 1; A_K+1 = - 2 A_K - K² - 1 (score: 5)

4, 13, 28, 49, 76, 109, 148, 193, 244, 301, 364, 433, 508, 589, 676, 769, 868, 973, 1084, 1201, 1324, 1453, 1588, 1729, 1876, 2029, 2188, 2353, 2524, 2701, 2884, 3073, 3268, 3469, 3676, 3889, ...

MCS7075 : A_K = 3 K² + 1 (score: 5)

4, 13, 29, 54, 90, 139, 203, 284, 384, 505, 649, 818, 1014, 1239, 1495, 1784, 2108, 2469, 2869, 3310, 3794, 4323, 4899, 5524, 6200, 6929, 7713, 8554, 9454, 10415, 11439, 12528, 13684, 14909, ...

MCS61969 : A₀ = -1; A_K+1 = A_K + K² (score: 4)

4, 13, 32, 65, 116, 189, 288, 417, 580, 781, 1024, 1313, 1652, 2045, 2496, 3009, 3588, 4237, 4960, 5761, 6644, 7613, 8672, 9825, 11076, 12429, 13888, 15457, 17140, 18941, 20864, 22913, 25092, ...

MCS31298 : A₀ = 0; A_K+1 = A_K + 2 K² + 1 (score: 5)

4, 13, 36, 89, 204, 445, 940, 1945, 3972, 8045, 16212, 32569, 65308, 130813, 261852, 523961, 1048212, 2096749, 4193860, 8388121, 16776684, 33553853, 67108236, 134217049, 268434724, 536870125, ...

MCS15656 : A₀ = 0; A_K+1 = 2 A_K + K² + 1 (score: 5)

4, 13, 40, 121, 364, 1093, 3280, 9841, 29524, 88573, 265720, 797161, 2391484, 7174453, 21523360, 64570081, 193710244, 581130733, 1743392200, 5230176601, 15690529804, 47071589413, 141214768240, ...

MCS979 (alias MCS62688) : A₀ = 0; A_N = 3 A_N-1 + 1 (score: 4)

(3^N-1)/2 (A3462)

4, 13, 43, 142, 469, 1549, 5116, 16897, 55807, 184318, 608761, 2010601, 6640564, 21932293, 72437443, 239244622, 790171309, 2609758549, 8619446956, 28468099417, 94023745207, 310539335038, ...

MCS1733126 : A₀ = 1; A₁ = 1; A_N = 3 A_N-1 + A_N-2 (score: 5)

Horadam sequence W_n(1, 1; 1, 3)

4, 13, 46, 193, 976, 5869, 41098, 328801, 2959228, 29592301, 325515334, 3906184033, 50780392456, 710925494413, ...

MCS7818 (alias MCS250192) : A₀ = 0; A_K+1 = K A_K + 2 K + 1 (score: 5)

4, 14, -22, -86, 152, 686, -1370, -6862, 15068, 82342, -195886, -1152790, 2938288, 18444638, -49950898, -332003486, 949067060, 6640069718, -19930408262, -146081533798, 458399390024, ...

MCS109313 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 - 2 (score: 5)

4, 14, 30, 52, 80, 114, 154, 200, 252, 310, 374, 444, 520, 602, 690, 784, 884, 990, 1102, 1220, 1344, 1474, 1610, 1752, 1900, 2054, 2214, 2380, 2552, 2730, 2914, 3104, 3300, 3502, 3710, 3924, ...

MCS7059 : A_K = 3 K² + K (score: 5)

4, 14, 35, 71, 126, 204, 309, 445, 616, 826, 1079, 1379, 1730, 2136, 2601, 3129, 3724, 4390, 5131, 5951, 6854, 7844, 8925, 10101, 11376, 12754, 14239, 15835, 17546, 19376, 21329, 23409, 25620, ...

MCS248084 : A₀ = 1; A_K+1 = A_K + 2 K² + K (score: 5)

4, -14, 40, -122, 364, -1094, 3280, -9842, 29524, -88574, 265720, -797162, 2391484, -7174454, 21523360, -64570082, 193710244, -581130734, 1743392200, -5230176602, 15690529804, -47071589414, ...

MCS15727 : A₀ = 0; A_N = - 3 A_N-1 - 2 (score: 5)

4, 14, 45, 139, 422, 1272, 3823, 11477, 34440, 103330, 310001, 930015, 2790058, 8370188, 25110579, 75331753, 225995276, 677985846, 2033957557, 6101872691, 18305618094, 54916854304, 164750562935, ...

MCS250784 : A₀ = 1; A_K+1 = 3 A_K + K + 1 (score: 5)

4, 14, 48, 164, 560, 1912, 6528, 22288, 76096, 259808, 887040, 3028544, 10340096, 35303296, 120532992, 411525376, 1405035520, 4797091328, 16378294272, 55918994432, 190919389184, 651839567872, ...

MCS53989 : A₀ = 0; A₁ = 1; A_N = 4 A_N-1 - 2 A_N-2 (score: 7)

Horadam sequence W_n(0, 1; -2, 4), Lucas sequence U_n(4, 2)

4, -14, 54, -272, 1630, -11412, 91294, -821648, 8216478, -90381260, 1084575118, -14099476536, 197392671502, ...

MCS503192 : A₀ = 1; A_K+1 = - K A_K - A_K - 2 (score: 5)

4, 14, 56, 271, 1576, 10768, 84576, 750425, 7419684, 80866110, 962973648, 12437791327, 173166104944, ...

MCS856897 : A₀ = 0; A₁ = 0; A_K+1 = K A_K - A_K-1 + K (score: 5)

4, -14, 64, -348, 2216, -16208, 134096, -1239280, 12660992, -141749472, 1726315648, -22725602368, 321611064448, ...

MCS6677 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K + 2 A_K-1 (score: 5)

4, 14, 64, 348, 2216, 16208, 134096, 1239280, 12660992, 141749472, 1726315648, 22725602368, 321611064448, ...

MCS3338 : A₀ = 0; A₁ = 1; A_K+1 = K A_K + 2 A_K-1 (score: 5)

4, 15, 34, 63, 104, 159, 230, 319, 428, 559, 714, 895, 1104, 1343, 1614, 1919, 2260, 2639, 3058, 3519, 4024, 4575, 5174, 5823, 6524, 7279, 8090, 8959, 9888, 10879, 11934, 13055, 14244, 15503, ...

MCS31564 : A₀ = 0; A_K+1 = A_K + K² - K - 1 (score: 5)

4, 15, 56, 209, 780, 2911, 10864, 40545, 151316, 564719, 2107560, 7865521, 29354524, 109552575, 408855776, 1525870529, 5694626340, 21252634831, 79315912984, 296011017105, ...

MCS13497 : A₀ = 0; A₁ = 1; A_N = 4 A_N-1 - A_N-2 (score: 6)

A1353

Horadam sequence W_n(0, 1; -1, 4), Lucas sequence U_n(4, 1)

4, 15, 58, 229, 912, 3643, 14566, 58257, 233020, 932071, 3728274, 14913085, 59652328, 238609299, 954437182, 3817748713, 15270994836, 61083979327, 244335917290, 977343669141, ...

MCS248752 : A₀ = 1; A_K+1 = 4 A_K - K (score: 5)

4, -15, 63, -331, 2048, -14668, 119391, -1089188, 11011270, -122213159, 1477569177, -19330612461, 272106143630, ...

MCS13705 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K + A_K-1 - 1 (score: 5)

4, 15, 64, 325, 1956, 13699, 109600, 986409, 9864100, 108505111, 1302061344, 16926797485, 236975164804, ...

MCS964 (alias MCS15796, MCS30864, MCS61729, MCS505488)

A₀ = 0; A_K+1 = K A_K + K (score: 3)

Distinct Nonempty Ordered Subsets of Set with N Elements (A7526)

4, 15, 64, 325, 1956, 13699, 109600, 986409, 9864100, 108505111, 1302061344, 16926797485, 236975164804, ...

MCS15652 : A₀ = 0; A_K+1 = K A_K + A_K + K + 1 (score: 5)

Distinct Nonempty Ordered Subsets of Set with N Elements (A7526)

4, -15, 74, -440, 3065, -24446, 219574, -2192675, 24094979, -288920174, 3753769587, -52528679239, 787641268411, ...

MCS6317110 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = - K A_K + A_K-2 (score: 5)

4, -15, 76, -455, 3186, -25487, 229384, -2293839, 25232230, -302786759, 3936227868, -55107190151, 826607852266, ...

MCS501144 : A₀ = 1; A_K+1 = - K A_K - 2 A_K + 1 (score: 5)

4, -15, 76, -455, 3186, -25487, 229384, -2293839, 25232230, -302786759, 3936227868, -55107190151, 826607852266, ...

MCS7833 (alias MCS13336) : A₀ = 0; A_K+1 = - K A_K - A_K + 1 (score: 4)

4, 15, 76, 455, 3186, 25487, 229384, 2293839, 25232230, 302786759, 3936227868, 55107190151, 826607852266, ...

MCS13328 : A₀ = 0; A₁ = 1; A_K+1 = K A_K + K A_K-1 (score: 5)

4, 16, 36, 64, 100, 144, 196, 256, 324, 400, 484, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, ...

MCS7051 : A_K = 4 K² (score: 5)

4, 16, 43, 91, 166, 274, 421, 613, 856, 1156, 1519, 1951, 2458, 3046, 3721, 4489, 5356, 6328, 7411, 8611, 9934, 11386, 12973, 14701, 16576, 18604, 20791, 23143, 25666, 28366, 31249, 34321, 37588, ...

MCS61980 : A₀ = 1; A_K+1 = A_K + 3 K² (score: 5)

4, -16, 64, -256, 1024, -4096, 16384, -65536, 262144, -1048576, 4194304, -16777216, 67108864, -268435456, 1073741824, -4294967296, 17179869184, -68719476736, 274877906944, ...

MCS248769 : A₀ = -1; A_N = - 4 A_N-1 (score: 5)

4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 1048576, 4194304, 16777216, 67108864, 268435456, 1073741824, 4294967296, 17179869184, 68719476736, 274877906944, ...

MCS62176 : A₀ = 1; A_N = 4 A_N-1 (score: 4)

Powers of 4 (A0302)

4, 16, 70, 358, 2158, 15118, 120958, 1088638, 10886398, 119750398, 1437004798, 18681062398, 261534873598, ...

MCS248144 : A₀ = 1; A_K+1 = K A_K + A_K + 2 K (score: 5)

4, 16, 72, 381, 2364, 16936, 137860, 1257685, 12714720, 141119616, 1706150124, 22321071241, 314201147512, ...

MCS856641 : A₀ = 0; A₁ = 0; A_K+1 = K A_K + A_K-1 + K (score: 5)

4, -17, 32, -88, 200, -497, 1184, -2876, 6924, -16737, 40384, -97520, 235408, -568353, 1372096, -3312564, 7997204, -19306993, 46611168, -112529352, 271669848, -655869073, 1583407968, -3822685036, ...

MCS3454593 : A₀ = 0; A₁ = 0; A_K+1 = - 2 A_K + A_K-1 - K (score: 5)

4, 17, 54, 145, 368, 945, 2530, 7073, 20412, 60049, 178478, 533169, 1596520, 4785713, 14352282, 43050817, 129145076, 387426321, 1162268326, 3486792401, 10460362464, 31381070257, 94143190994, ...

MCS64207318 : A₀ = 1; A_K+1 = 3 A_K - 2 K³ + 3 K² + 3 K + 1 (score: 15)

3^N+N³ (A1585)

4, 17, 70, 283, 1136, 4549, 18202, 72815, 291268, 1165081, 4660334, 18641347, 74565400, 298261613, 1193046466, 4772185879, 19088743532, 76354974145, 305419896598, ...

MCS248736 : A₀ = 1; A_K+1 = 4 A_K + K (score: 5)

4, 17, 72, 305, 1292, 5473, 23184, 98209, 416020, 1762289, 7465176, 31622993, 133957148, 567451585, 2403763488, 10182505537, 43133785636, 182717648081, 774004377960, ...

MCS6748 : A₀ = 0; A₁ = 1; A_N = 4 A_N-1 + A_N-2 (score: 6)

Value of Fibonacci polynomials when x=4 (A1076)

Horadam sequence W_n(0, 1; 1, 4), Lucas sequence U_n(4, -1)

4, 17, 86, 517, 3620, 28961, 260650, 2606501, 28671512, 344058145, 4472755886, 62618582405, 939278736076, ...

MCS7828 : A₀ = 0; A_K+1 = K A_K + 2 A_K + 1 (score: 5)

4, 17, 86, 517, 3620, 28961, 260650, 2606501, 28671512, 344058145, 4472755886, 62618582405, 939278736076, ...

MCS250401 : A₀ = -1; A_K+1 = K A_K + A_K + 1 (score: 5)

4, -17, 89, -551, 3946, -32119, 293017, -2962289, 32878196, -397500641, 5200386529, -73202912047, ...

MCS3459462 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K - A_K + A_K-1 (score: 5)

4, -18, 15, -41, 47, -98, 134, -244, 365, -623, 973, -1612, 2568, -4198, 6747, -10965, 17691, -28678, 46346, -75048, 121369, -196443, 317785, -514256, 832012, -1346298, 2178279, -3524609, 5702855, ...

MCS13750 : A₀ = 0; A₁ = 1; A_K+1 = - A_K + A_K-1 - K - 1 (score: 5)

4, -18, 24, -62, 108, -234, 448, -918, 1812, -3650, 7272, -14574, 29116, -58266, 116496, -233030, 466020, -932082, 1864120, -3728286, 7456524, -14913098, 29826144, -59652342, 119304628, ...

MCS15541 : A₀ = 0; A_K+1 = - 2 A_K - 2 K (score: 4)

4, 18, 48, 100, 180, 294, 448, 648, 900, 1210, 1584, 2028, 2548, 3150, 3840, 4624, 5508, 6498, 7600, 8820, 10164, 11638, 13248, 15000, 16900, 18954, 21168, 23548, 26100, 28830, 31744, 34848, ...

MCS3526 : A_K = K³ - K² (score: 5)

4, 18, 80, 356, 1584, 7048, 31360, 139536, 620864, 2762528, 12291840, 54692416, 243353344, 1082798208, 4817899520, 21437194496, 95384577024, 424412697088, ...

MCS26994 : A₀ = 0; A₁ = 1; A_N = 4 A_N-1 + 2 A_N-2 (score: 7)

Horadam sequence W_n(0, 1; 2, 4), Lucas sequence U_n(4, -2)

4, -18, 88, -530, 3708, -29666, 266992, -2669922, 29369140, -352429682, 4581585864, -64142202098, 962133031468, ...

MCS7857 (alias MCS31441, MCS125720, MCS251441, MCS503064)

A₀ = 0; A_K+1 = - K A_K - 2 (score: 4)

4, -18, 129, -1157, 12732, -165510, 2482657, -42205161, 801898068, -16839859418, 387316766625, ...

MCS498264 : A₀ = 1; A_K+1 = - 2 K A_K - A_K + K (score: 5)

4, 19, 118, 949, 9496, 113959, 1595434, 25526953, 459485164, 9189703291, 202173472414, ...

MCS15634 (alias MCS250152) : A₀ = 0; A_K+1 = 2 K A_K + K + 1 (score: 5)

4, 21, 56, 115, 204, 329, 496, 711, 980, 1309, 1704, 2171, 2716, 3345, 4064, 4879, 5796, 6821, 7960, 9219, 10604, 12121, 13776, 15575, 17524, 19629, 21896, 24331, 26940, 29729, 32704, 35871, ...

MCS14124 : A_K = K³ - 2 K (score: 5)

4, 21, 148, 1333, 14664, 190633, 2859496, 48611433, 923617228, 19395961789, 446107121148, ...

MCS250664 : A₀ = 1; A_K+1 = 2 K A_K - A_K + 1 (score: 5)

4, 21, 148, 1333, 14664, 190633, 2859496, 48611433, 923617228, 19395961789, 446107121148, ...

MCS15650 : A₀ = 0; A_K+1 = 2 K A_K + A_K + 1 (score: 5)

4, 22, 157, 1417, 15592, 202702, 3040537, 51689137, 982093612, 20623965862, 474351214837, ...

MCS248104 : A₀ = 1; A_K+1 = 2 K A_K + A_K + K (score: 5)

4, -23, 128, -880, 6904, -61265, 605736, -6601842, 78616356, -1015410799, 14137134816, -211041611456, ...

MCS858977 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K - A_K-1 - K (score: 5)

4, -23, 157, -1418, 15592, -202703, 3040537, -51689138, 982093612, -20623965863, 474351214837, ...

MCS496472 : A₀ = 1; A_K+1 = - 2 K A_K + A_K - K (score: 5)

4, 25, 226, 2713, 40696, 732529, 15383110, 369194641, 9968255308, 299047659241, ...

MCS3907 (alias MCS62520) : A₀ = 0; A_K+1 = 3 K A_K + 1 (score: 5)

4, -28, 280, -3640, 58240, -1106560, 24344320, -608608000, 17041024000, -528271744000, ...

MCS249080 : A₀ = 1; A_K+1 = - 3 K A_K - A_K (score: 5)

4, 28, 280, 3640, 58240, 1106560, 24344320, 608608000, 17041024000, 528271744000, ...

MCS62008 : A₀ = 1; A_K+1 = 3 K A_K + A_K (score: 5)

4, 29, -29, -233, 260, 2329, -2861, -27949, 37192, 391285, -557881, -6260561, 9483976, 112690097, -180195545, -2253801941, 3784106444, 49583642701, -87034448213, ...

MCS1753197 : A₀ = -1; A₁ = -1; A_K+1 = - K A_K-1 - 1 (score: 5)

4, -29, 260, -2861, 37192, -557881, 9483976, -180195545, 3784106444, -87034448213, ...

MCS31557 : A₀ = 0; A_K+1 = - 2 K A_K + A_K - 1 (score: 5)

4, -30, 232, -2330, 27948, -391286, 6260560, -112690098, 2253801940, -49583642702, ...

MCS30901 (alias MCS494424) : A₀ = 0; A_K+1 = - 2 K A_K - 2 K (score: 5)

4, -39, 464, -6965, 125364, -2632651, 63183616, -1705957641, 51178729220, ...

MCS15471 (alias MCS247544) : A₀ = 0; A_K+1 = - 3 K A_K - K (score: 5)

4, 40, 12, -308, -416, 2664, 7240, -24728, -118848, 227344, 2010064, -1627440, -35798528, -6504608, 673667424, 803759584, -13343256320, -31025967168, 275868928192, ...

MCS107617 : A₀ = 0; A₁ = 1; A_K+1 = A_K - K A_K-1 - A_K-1 (score: 5)

4, 40, 12, -308, -416, 2664, 7240, -24728, -118848, 227344, 2010064, -1627440, -35798528, -6504608, 673667424, 803759584, -13343256320, -31025967168, 275868928192, ...

MCS430105 : A₀ = -1; A₁ = 0; A_K+1 = A_K - K A_K-1 (score: 5)

4, -50, 258, -1862, 14824, -133506, 1334950, -14684582, 176214828, -2290792946, 32071101034, -481066515750, ...

MCS15469 (alias MCS123756) : A₀ = 0; A_K+1 = - K A_K - K² - K (score: 5)

5, 0, -11, 5, 22, -21, -39, 64, 57, -167, -50, 391, -67, -832, 525, 1597, -1882, -2669, 5361, 3456, -13391, -1551, 30238, -10289, -62027, 50816, 113765, -163659, -176714, 441083, 189769, -1058880, ...

MCS792097 : A₀ = 0; A₁ = 1; A₂ = 1; A_N = - 2 A_N-2 + A_N-3 (score: 5)

5, 0, 17, -8, 53, -56, 177, -272, 645, -1168, 2481, -4792, 9781, -19336, 38929, -77568, 155461, -310560, 621521, -1242600, 2485685, -4970840, 9942257, -19883888, 39768453, -79536176, 159073137, ...

MCS31320 : A₀ = 0; A_K+1 = - 2 A_K + K² + 1 (score: 5)

5, 0, 25, 0, 125, 0, 625, 0, 3125, 0, 15625, 0, 78125, 0, 390625, 0, 1953125, 0, 9765625, 0, 48828125, 0, 244140625, 0, 1220703125, 0, 6103515625, 0, 30517578125, 0, 152587890625, 0, 762939453125, ...

MCS1671 : A₀ = 0; A₁ = 1; A_N = 5 A_N-2 (score: 6)

(Not in OEIS)

Horadam sequence W_n(0, 1; 5, 0), Lucas sequence U_n(0, -5)

5, 0, 45, 0, 585, 0, 9945, 0, 208845, 0, 5221125, 0, 151412625, 0, 4996616625, 0, 184874815125, 0, ...

MCS53378 : A₀ = 0; A₁ = 1; A_K+1 = 2 K A_K-1 + A_K-1 (score: 5)

5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, ...

MCS427022 : A₀ = 1; A₁ = 5; A_N = A_N-2 (score: 5)

Horadam sequence W_n(1, 5; 1, 0)

5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, 5, -1, -5, 1, ...

MCS427534 : A₀ = 1; A₁ = 5; A_N = - A_N-2 (score: 5)

Horadam sequence W_n(1, 5; -1, 0)

5, 1, -7, -7, 5, 13, 1, -19, -15, 17, 33, -3, -51, -31, 53, 81, -23, -135, -59, 157, 193, -99, -351, -95, 449, 445, -355, -895, -91, 1249, 985, -1159, -2235, 173, 3393, 2061, -3567, -5455, 1505, ...

MCS26789430 : A₀ = 1; A₁ = 1; A₂ = 1; A_N = - A_N-2 - A_N-3 - 1 (score: 5)

5, 1, -11, -3, 21, 5, -43, -11, 85, 21, -171, -43, 341, 85, -683, -171, 1365, 341, -2731, -683, 5461, 1365, -10923, -2731, 21845, 5461, -43691, -10923, 87381, 21845, -174763, -43691, 349525, ...

MCS14035990 : A₀ = 1; A₁ = 0; A_N = - 2 A_N-2 - 1 (score: 5)

5, 1, -16, 13, 35, -74, -31, 253, -160, -599, 1079, 718, -3955, 1801, 10064, -15467, -14725, 61126, -16951, -166427, 217280, 282001, -933841, 87838, 2713685, -2977199, -5163856, 14095453, 1396115, ...

MCS13519 : A₀ = 0; A₁ = 1; A_N = - A_N-1 - 3 A_N-2 (score: 5)

A214733

Horadam sequence W_n(0, 1; -3, -1), Lucas sequence U_n(-1, 3)

5, -1, -29, 29, 167, -407, -1105, 5165, 6979, -68971, -21769, 987349, -660829, -15136771, 26370847, 246091013, -747137125, -4174683155, 19864562759, 71978466629, -528863410109, ...

MCS108225 : A₀ = 0; A₁ = 1; A_K+1 = - A_K - K A_K-1 - K (score: 5)

5, -1, -31, -1, 209, -1, -1891, -1, 20789, -1, -270271, -1, 4054049, -1, -68918851, -1, 1309458149, -1, -27498621151, -1, 632468286449, -1, ...

MCS107329 (alias MCS3434550) : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 + A_K-1 - K (score: 5)

5, 2, -17, -12, 25, 14, -61, -40, 109, 66, -233, -148, 449, 278, -917, -576, 1813, 1130, -3649, -2284, 7273, 4542, -14573, -9112, 29117, 18194, -58265, -36420, 116497, 72806, -233029, -145648, ...

MCS6870541 : A₀ = -1; A₁ = -1; A_K+1 = - 2 A_K-1 - K (score: 5)

5, -2, 31, 2, 121, -26, 395, -278, 1285, -1570, 4471, -7214, 16625, -30506, 64387, -124678, 254269, -502706, 1012271, -2016542, 4042345, -8074042, 16160251, -32306678, 64628981, -129240386, ...

MCS124292 : A₀ = 1; A_K+1 = - 2 A_K + K³ (score: 5)

5, -3, -3, -11, 5, 5, 21, -11, -11, -43, 21, 21, 85, -43, -43, -171, 85, 85, 341, -171, -171, -683, 341, 341, 1365, -683, -683, -2731, 1365, 1365, 5461, -2731, -2731, -10923, 5461, 5461, 21845, ...

MCS1671521 : A₀ = 0; A₁ = 0; A₂ = 1; A_N = - 2 A_N-3 - 1 (score: 5)

5, -3, -3, 13, -19, 13, 13, -51, 77, -51, -51, 205, -307, 205, 205, -819, 1229, -819, -819, 3277, -4915, 3277, 3277, -13107, 19661, -13107, -13107, 52429, -78643, 52429, 52429, -209715, 314573, ...

MCS811169 : A₀ = 0; A₁ = 0; A₂ = 1; A_N = - A_N-1 + 2 A_N-3 (score: 5)

5, 3, 9, 7, 13, 11, 17, 15, 21, 19, 25, 23, 29, 27, 33, 31, 37, 35, 41, 39, 45, 43, 49, 47, 53, 51, 57, 55, 61, 59, 65, 63, 69, 67, 73, 71, 77, 75, 81, 79, 85, 83, 89, 87, 93, 91, 97, 95, 101, 99, ...

MCS249200 : A₀ = 1; A_K+1 = - A_K + 4 K (score: 5)

5, -3, -11, 5, 21, -11, -43, 21, 85, -43, -171, 85, 341, -171, -683, 341, 1365, -683, -2731, 1365, 5461, -2731, -10923, 5461, 21845, -10923, -43691, 21845, 87381, -43691, -174763, 87381, 349525, ...

MCS6853 (alias MCS1754497) : A₀ = 0; A₁ = 1; A_N = - 2 A_N-2 - 1 (score: 4)

5, 3, -26, -19, 181, 151, -1630, -1511, 17929, 18131, -233078, -253835, 3496169, 4061359, -59434874, -73104463, 1129262605, 1462089259, -23714514706, -32165963699, 545433838237, 771983128775, ...

MCS3506390 : A₀ = 1; A₁ = 0; A_K+1 = - K A_K-1 - 1 (score: 5)

5, 3, 27, -3, 199, -215, 2015, -4155, 26331, -76179, 418495, -1484987, 7762427, -31522203, 163483479, -730883115, 3837069235, -18454731515, 99033185471, -505037278779, ...

MCS865289 : A₀ = 0; A₁ = 0; A_K+1 = - A_K + K A_K-1 + K (score: 5)

5, 4, -5, -2, 17, 12, -25, -14, 61, 40, -109, -66, 233, 148, -449, -278, 917, 576, -1813, -1130, 3649, 2284, -7273, -4542, 14573, 9112, -29117, -18194, 58265, 36420, -116497, -72806, 233029, ...

MCS3427078 : A₀ = 1; A₁ = 1; A_K+1 = - 2 A_K-1 + K (score: 4)

5, 4, 15, 14, 37, 36, 83, 82, 177, 176, 367, 366, 749, 748, 1515, 1514, 3049, 3048, 6119, 6118, 12261, 12260, 24547, 24546, 49121, 49120, 98271, 98270, 196573, 196572, 393179, 393178, 786393, ...

MCS1713413 : A₀ = 0; A₁ = -1; A_K+1 = 2 A_K-1 + K (score: 5)

5, 4, 17, 12, 41, 20, 85, 16, 169, -32, 345, -208, 749, -732, 1737, -2180, 4241, -6060, 10701, -16320, 27505, -43296, 71377, -114048, 186101, -299420, 486305, -784884, 1272089, -2056012, 3329125, ...

MCS13512 : A₀ = 0; A₁ = 1; A_K+1 = - A_K + A_K-1 + K² (score: 5)

5, -4, -29, 29, 233, -260, -2329, 2861, 27949, -37192, -391285, 557881, 6260561, -9483976, -112690097, 180195545, 2253801941, -3784106444, -49583642701, 87034448213, ...

MCS868406 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K-1 + 1 (score: 4)

5, -4, -29, 29, 233, -260, -2329, 2861, 27949, -37192, -391285, 557881, 6260561, -9483976, -112690097, 180195545, 2253801941, -3784106444, -49583642701, 87034448213, ...

MCS108609 (alias MCS3475510) : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 + A_K-1 + 1 (score: 5)

5, 5, -3, -11, -11, 5, 21, 21, -11, -43, -43, 21, 85, 85, -43, -171, -171, 85, 341, 341, -171, -683, -683, 341, 1365, 1365, -683, -2731, -2731, 1365, 5461, 5461, -2731, -10923, -10923, 5461, ...

MCS835761 : A₀ = 0; A₁ = 1; A₂ = 1; A_N = - 2 A_N-3 - 1 (score: 5)

5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, ...

MCS887 (alias MCS61959) : A_N = 5 (score: 5)

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