Minimally Complex Sequences

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2, 5, 16, 65, 326, 1957, 13700, 109601, 986410, 9864101, 108505112, 1302061345, 16926797486, 236975164805, ...

MCS125200 : A₀ = 1; A_K+1 = K A_K + A_K + 1 (score: 4)

Distinct Ordered Subsets of Set with N Elements (A0522)

2, 5, 16, 65, 326, 1957, 13700, 109601, 986410, 9864101, 108505112, 1302061345, 16926797486, 236975164805, ...

MCS15660 : A₀ = 0; A_K+1 = K A_K - 2 A_K + 1 (score: 5)

Distinct Ordered Subsets of Set with N Elements (A0522)

2, 5, 16, 66, 335, 2026, 14248, 114319, 1030897, 10323218, 113669717, 1365067501, 17756200731, 248700479951, ...

MCS1577222 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = K A_K + A_K-2 (score: 5)

2, -5, 17, -56, 185, -611, 2018, -6665, 22013, -72704, 240125, -793079, 2619362, -8651165, 28572857, -94369736, 311682065, -1029415931, 3399929858, -11229205505, 37087546373, -122491844624, ...

MCS1735808 : A₀ = 1; A₁ = 2; A_N = - 3 A_N-1 + A_N-2 (score: 5)

Horadam sequence W_n(1, 2; 1, -3)

2, 5, 17, 73, 382, 2365, 16937, 137861, 1257686, 12714721, 141119617, 1706150125, 22321071242, 314201147513, ...

MCS854278 : A₀ = 1; A₁ = 1; A_K+1 = K A_K + A_K-1 (score: 4)

2, 5, 17, 73, 382, 2365, 16937, 137861, 1257686, 12714721, 141119617, 1706150125, 22321071242, 314201147513, ...

MCS860736 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + A_K + A_K-1 (score: 5)

2, 5, 17, 73, 382, 2365, 16937, 137861, 1257686, 12714721, 141119617, 1706150125, 22321071242, 314201147513, ...

MCS3459334 : A₀ = 1; A₁ = 1; A_K+1 = K A_K - A_K + A_K-1 (score: 5)

2, -5, 17, -81, 468, -3196, 25099, -222696, 2201860, -23997765, 285771319, -3691029383, 51388640042, -767138571248, ...

MCS13709 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K - A_K-1 - 1 (score: 5)

2, 5, 18, 63, 190, 505, 1226, 2795, 6102, 12933, 26866, 55063, 111854, 225905, 454554, 912483, 1829062, 3663037, 7331906, 14670671, 29349342, 58707945, 117426538, 234865243, 469744310, 939504245, ...

MCS62084 : A₀ = 1; A_K+1 = 2 A_K + K³ (score: 5)

2, -5, 18, -85, 492, -3359, 26380, -234061, 2314230, -25222469, 300355398, -3879397705, 54011212472, -806288789375, ...

MCS13453 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K + A_K - A_K-1 (score: 5)

2, -5, 18, -85, 492, -3359, 26380, -234061, 2314230, -25222469, 300355398, -3879397705, 54011212472, -806288789375, ...

MCS3421718 : A₀ = 1; A₁ = 0; A_K+1 = - K A_K - A_K-1 (score: 5)

2, 5, 18, 85, 492, 3359, 26380, 234061, 2314230, 25222469, 300355398, 3879397705, 54011212472, 806288789375, ...

MCS6726 : A₀ = 0; A₁ = 1; A_K+1 = K A_K + A_K - A_K-1 (score: 5)

2, 5, 18, 85, 492, 3359, 26380, 234061, 2314230, 25222469, 300355398, 3879397705, 54011212472, 806288789375, ...

MCS427649 : A₀ = -1; A₁ = 0; A_K+1 = K A_K - A_K-1 (score: 5)

2, 5, 18, 87, 518, 3621, 28962, 260651, 2606502, 28671513, 344058146, 4472755887, 62618582406, 939278736077, ...

MCS248528 : A₀ = 1; A_K+1 = K A_K + 2 A_K - K (score: 5)

2, 5, 18, 87, 518, 3621, 28962, 260651, 2606502, 28671513, 344058146, 4472755887, 62618582406, 939278736077, ...

MCS15654 : A₀ = 0; A_K+1 = K A_K + A_K - K + 1 (score: 5)

2, -5, 18, -103, 806, -7957, 94678, -1317535, 20985882, -376428341, 7507580938, -164790352295, ...

MCS855392 : A₀ = 1; A₁ = 2; A_K+1 = - 2 K A_K - A_K-1 (score: 5)

2, 5, 19, 93, 553, 3852, 30723, 275954, 2755688, 30281845, 363106186, 4717624730, 66016464375, 989883859439, ...

MCS197169 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = K A_K - A_K-2 (score: 5)

2, 5, 21, 42, 82, 133, 209, 302, 426, 573, 757, 970, 1226, 1517, 1857, 2238, 2674, 3157, 3701, 4298, 4962, 5685, 6481, 7342, 8282, 9293, 10389, 11562, 12826, 14173, 15617, 17150, 18786, 20517, ...

MCS126340 : A₀ = 1; A_K+1 = - A_K + K³ - 1 (score: 5)

2, -5, 22, -107, 646, -4517, 36142, -325271, 3252718, -35779889, 429358678, -5581662803, 78143279254, ...

MCS31593 : A₀ = 0; A_K+1 = - K A_K - A_K + K - 1 (score: 5)

2, 5, 22, 137, 1118, 11317, 136922, 1928225, 30988522, 559721621, 11225420942, 247518982345, ...

MCS427168 : A₀ = 1; A₁ = 2; A_K+1 = 2 K A_K + A_K-1 (score: 5)

2, -5, 23, -119, 738, -5284, 43011, -392382, 3966832, -44027533, 532297229, -6963891509, 98026778356, ...

MCS13577 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K + A_K-1 + 1 (score: 5)

2, 6, 2, -10, -14, 6, 34, 22, -46, -90, 2, 182, 178, -186, -542, -170, 914, 1254, -574, -3082, -1934, 4230, 8098, -362, -16558, -15834, 17282, 48950, 14386, -83514, -112286, 54742, 279314, 169830, ...

MCS13773846 : A₀ = 1; A₁ = 0; A_N = A_N-1 - 2 A_N-2 (score: 5)

Horadam sequence W_n(1, 0; -2, 1)

2, 6, 4, -2, 4, 18, 8, -18, 4, 58, 16, -90, -4, 210, 40, -386, -44, 810, 128, -1578, -212, 3202, 472, -6354, -892, 12762, 1840, -25466, -3620, 50994, 7304, -101922, -14540, 203914, 29152, -407754, ...

MCS6859526 : A₀ = 1; A₁ = 1; A_K+1 = - 2 A_K-1 + 2 K (score: 5)

2, 6, -4, -40, -12, 308, 416, -2664, -7240, 24728, 118848, -227344, -2010064, 1627440, 35798528, 6504608, -673667424, -803759584, 13343256320, 31025967168, -275868928192, ...

MCS3440854 : A₀ = 1; A₁ = 0; A_K+1 = A_K - K A_K-1 (score: 5)

2, -6, -4, 40, -12, -308, 416, 2664, -7240, -24728, 118848, 227344, -2010064, -1627440, 35798528, -6504608, -673667424, 803759584, 13343256320, -31025967168, -275868928192, ...

MCS3457238 : A₀ = 1; A₁ = 0; A_K+1 = - A_K - K A_K-1 (score: 5)

2, 6, -6, -14, 10, 26, -22, -54, 42, 106, -86, -214, 170, 426, -342, -854, 682, 1706, -1366, -3414, 2730, 6826, -5462, -13654, 10922, 27306, -21846, -54614, 43690, 109226, -87382, -218454, 174762, ...

MCS27333 : A₀ = 0; A₁ = 1; A_N = - 2 A_N-2 - 2 (score: 5)

2, -6, 8, -4, -8, 24, -32, 16, 32, -96, 128, -64, -128, 384, -512, 256, 512, -1536, 2048, -1024, -2048, 6144, -8192, 4096, 8192, -24576, 32768, -16384, -32768, 98304, -131072, 65536, 131072, ...

MCS3453632 : A₀ = 1; A₁ = 2; A_N = - 2 A_N-1 - 2 A_N-2 (score: 5)

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

2, 6, 8, -5, -12, 84, 160, -675, -1500, 7546, 18144, -97929, -253820, 1469160, 4061376, -24975431, -73104444, 474533550, 1462089280, -9965204109, -32165963676, 229199695036, 771983128800, ...

MCS26641 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 + K² (score: 5)

2, -6, 8, -13, 14, -20, 20, -27, 26, -34, 32, -41, 38, -48, 44, -55, 50, -62, 56, -69, 62, -76, 68, -83, 74, -90, 80, -97, 86, -104, 92, -111, 98, -118, 104, -125, 110, -132, 116, -139, 122, -146, ...

MCS3454656 : A₀ = 1; A₁ = 2; A_K+1 = - 2 A_K - A_K-1 - K (score: 5)

2, -6, 8, -22, 36, -82, 152, -318, 620, -1258, 2496, -5014, 10004, -20034, 40040, -80110, 160188, -320410, 640784, -1281606, 2563172, -5126386, 10252728, -20505502, 41010956, -82021962, 164043872, ...

MCS994657 : A₀ = -1; A_K+1 = - 2 A_K - 2 K (score: 5)

2, -6, 9, -13, 16, -20, 23, -27, 30, -34, 37, -41, 44, -48, 51, -55, 58, -62, 65, -69, 72, -76, 79, -83, 86, -90, 93, -97, 100, -104, 107, -111, 114, -118, 121, -125, 128, -132, 135, -139, 142, ...

MCS3517632 : A₀ = 1; A₁ = 2; A_N = - 2 A_N-1 - A_N-2 - 1 (score: 5)

2, 6, 9, 15, 20, 28, 35, 45, 54, 66, 77, 91, 104, 120, 135, 153, 170, 190, 209, 231, 252, 276, 299, 325, 350, 378, 405, 435, 464, 496, 527, 561, 594, 630, 665, 703, 740, 780, 819, 861, 902, 946, ...

MCS7896 (alias MCS31148) : A₀ = 0; A_K+1 = - A_K + K² - 1 (score: 4)

2, 6, 10, 12, 12, 12, 14, 18, 22, 24, 24, 24, 26, 30, 34, 36, 36, 36, 38, 42, 46, 48, 48, 48, 50, 54, 58, 60, 60, 60, 62, 66, 70, 72, 72, 72, 74, 78, 82, 84, 84, 84, 86, 90, 94, 96, 96, 96, 98, ...

MCS1723073 : A₀ = 0; A₁ = 0; A_K+1 = A_K - A_K-1 + 2 K (score: 5)

2, 6, 10, 14, 20, 28, 36, 44, 54, 66, 78, 90, 104, 120, 136, 152, 170, 190, 210, 230, 252, 276, 300, 324, 350, 378, 406, 434, 464, 496, 528, 560, 594, 630, 666, 702, 740, 780, 820, 860, 902, 946, ...

MCS856865 (alias MCS858913) : A₀ = 0; A₁ = 0; A_K+1 = - A_K-1 + K² + K (score: 5)

2, 6, 10, 20, 30, 52, 74, 120, 166, 260, 354, 544, 734, 1116, 1498, 2264, 3030, 4564, 6098, 9168, 12238, 18380, 24522, 36808, 49094, 73668, 98242, 147392, 196542, 294844, 393146, 589752, 786358, ...

MCS6698 : A₀ = 0; A₁ = 1; A_K+1 = 2 A_K-1 + 2 K (score: 5)

2, -6, 10, -22, 42, -86, 170, -342, 682, -1366, 2730, -5462, 10922, -21846, 43690, -87382, 174762, -349526, 699050, -1398102, 2796202, -5592406, 11184810, -22369622, 44739242, -89478486, ...

MCS7861 (alias MCS864897, MCS1006273, MCS2012546)

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

Horadam sequence W_n(-1, 0; 2, -1)

2, 6, 10, 23, 36, 76, 116, 237, 358, 722, 1086, 2179, 3272, 6552, 9832, 19673, 29514, 59038, 88562, 177135, 265708, 531428, 797148, 1594309, 2391470, 4782954, 7174438, 14348891, 21523344, ...

MCS428481 : A₀ = 0; A₁ = 0; A_K+1 = 3 A_K-1 + K (score: 5)

2, 6, 11, 17, 24, 32, 41, 51, 62, 74, 87, 101, 116, 132, 149, 167, 186, 206, 227, 249, 272, 296, 321, 347, 374, 402, 431, 461, 492, 524, 557, 591, 626, 662, 699, 737, 776, 816, 857, 899, 942, 986, ...

MCS1006145 : A₀ = -1; A_K+1 = A_K + K - 2 (score: 5)

2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, ...

MCS1764 (alias MCS1766, MCS1938, MCS7778, MCS15698)

A_K = K² + K (score: 3)

Semisquare (or Promic) numbers (A2378)

2, 6, 12, 23, 38, 60, 88, 125, 170, 226, 292, 371, 462, 568, 688, 825, 978, 1150, 1340, 1551, 1782, 2036, 2312, 2613, 2938, 3290, 3668, 4075, 4510, 4976, 5472, 6001, 6562, 7158, 7788, 8455, 9158, ...

MCS13576 : A₀ = 0; A₁ = 1; A_K+1 = A_K-1 + K² + 1 (score: 5)

2, 6, 12, 32, 70, 204, 504, 1648, 4554, 16500, 50116, 198024, 651534, 2772364, 9773040, 44357856, 166141714, 798441444, 3156692604, 15968828920, 66290544726, 351314236284, ...

MCS26784 : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 + 2 K (score: 5)

2, 6, 12, 35, 78, 252, 632, 2277, 6330, 25058, 75972, 325767, 1063622, 4886520, 17017968, 83070857, 306323442, 1578346302, 6126468860, 33145272363, 134782314942, 762341264372, ...

MCS214025 : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 + K (score: 4)

2, 6, 13, 23, 36, 52, 71, 93, 118, 146, 177, 211, 248, 288, 331, 377, 426, 478, 533, 591, 652, 716, 783, 853, 926, 1002, 1081, 1163, 1248, 1336, 1427, 1521, 1618, 1718, 1821, 1927, 2036, 2148, ...

MCS250480 : A₀ = 1; A_K+1 = A_K + 3 K + 1 (score: 5)

2, 6, 13, 25, 45, 78, 132, 220, 363, 595, 971, 1580, 2566, 4162, 6745, 10925, 17689, 28634, 46344, 75000, 121367, 196391, 317783, 514200, 832010, 1346238, 2178277, 3524545, 5702853, 9227430, ...

MCS6890509 : A₀ = -1; A₁ = -1; A_K+1 = A_K + A_K-1 + K (score: 5)

2, 6, 13, 29, 60, 124, 251, 507, 1018, 2042, 4089, 8185, 16376, 32760, 65527, 131063, 262134, 524278, 1048565, 2097141, 4194292, 8388596, 16777203, 33554419, 67108850, 134217714, 268435441, ...

MCS13458 : A₀ = 0; A₁ = 1; A_K+1 = A_K + 2 A_K-1 + K (score: 5)

2, -6, 13, -44, 121, -430, 1397, -5268, 19237, -77186, 308029, -1311448, 5623853, -25295574, 115277221, -545301980, 2620291957, -12981029578, 65386868717, -337988489856, ...

MCS3518502 : A₀ = 1; A₁ = 1; A_K+1 = - A_K + K A_K-1 - 1 (score: 5)

2, 6, 14, 26, 44, 68, 100, 140, 190, 250, 322, 406, 504, 616, 744, 888, 1050, 1230, 1430, 1650, 1892, 2156, 2444, 2756, 3094, 3458, 3850, 4270, 4720, 5200, 5712, 6256, 6834, 7446, 8094, 8778, ...

MCS856609 (alias MCS858657) : A₀ = 0; A₁ = 0; A_K+1 = A_K-1 + K² + K (score: 5)

2, 6, 14, 28, 52, 92, 158, 266, 442, 728, 1192, 1944, 3162, 5134, 8326, 13492, 21852, 35380, 57270, 92690, 150002, 242736, 392784, 635568, 1028402, 1664022, 2692478, 4356556, 7049092, 11405708, ...

MCS1723009 : A₀ = 0; A₁ = 0; A_K+1 = A_K + A_K-1 + 2 K (score: 5)

2, 6, 14, 30, 62, 126, 254, 510, 1022, 2046, 4094, 8190, 16382, 32766, 65534, 131070, 262142, 524286, 1048574, 2097150, 4194302, 8388606, 16777214, 33554430, 67108862, 134217726, 268435454, ...

MCS1962 (alias MCS251201, MCS502402) : A₀ = 0; A_N = 2 A_N-1 + 2 (score: 4)

2, 6, 15, 31, 56, 92, 141, 205, 286, 386, 507, 651, 820, 1016, 1241, 1497, 1786, 2110, 2471, 2871, 3312, 3796, 4325, 4901, 5526, 6202, 6931, 7715, 8556, 9456, 10417, 11441, 12530, 13686, 14911, ...

MCS30984 : A₀ = 1; A_K+1 = A_K + K² (score: 3)

Pyramid numbers Plus One (A56520)

2, 6, 15, 36, 90, 234, 651, 1896, 5886, 18990, 64779, 227916, 842166, 3190866, 12632535, 51053904, 214753146, 918970326, 4080309831, 18379406580, 85686506514, 404346944826, ...

MCS859153 : A₀ = -1; A₁ = 0; A_K+1 = K A_K-1 + 3 K (score: 7)

Not related to Pell numbers

2, 6, 15, 37, 90, 218, 527, 1273, 3074, 7422, 17919, 43261, 104442, 252146, 608735, 1469617, 3547970, 8565558, 20679087, 49923733, 120526554, 290976842, 702480239, 1695937321, 4094354882, ...

MCS1741952 : A₀ = 1; A₁ = 2; A_N = 2 A_N-1 + A_N-2 + 1 (score: 5)

Related to Pell numbers (A98790)

2, 6, 15, 40, 100, 276, 749, 2272, 6822, 22820, 75163, 273984, 977288, 3835972, 14659545, 61375808, 249212554, 1104764868, 4735038887, 22095297760, 99435817068, 486096551204, ...

MCS852518 : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 + K² (score: 5)

2, 6, 15, 40, 104, 273, 714, 1870, 4895, 12816, 33552, 87841, 229970, 602070, 1576239, 4126648, 10803704, 28284465, 74049690, 193864606, 507544127, 1328767776, 3478759200, 9107509825, 23843770274, ...

MCS100945 (alias MCS6460513) : A₀ = 0; A₁ = 1; A₂ = 2; A_N = 2 A_N-1 + 2 A_N-2 - A_N-3 (score: 7)

Golden rectangle: product of consecutive Fibonacci numbers (A1654)

2, 6, 15, 43, 123, 387, 1255, 4359, 15663, 59263, 231567, 942735, 3953119, 17151423, 76448223, 350871007, 1650490815, 7966168959, 39325494463, 198648873663, ...

MCS53824 : A₀ = 0; A₁ = 1; A_K+1 = A_K + K A_K-1 + K (score: 5)

2, 6, 15, 46, 137, 460, 1557, 5698, 21269, 83948, 339177, 1430502, 6178981, 27636512, 126500209, 596320914, 2873324677, 14203422044, 71669915585, 369941778510, ...

MCS870409 : A₀ = 0; A₁ = 0; A_K+1 = A_K + K A_K-1 + 1 (score: 5)

2, 6, 16, 38, 84, 178, 368, 750, 1516, 3050, 6120, 12262, 24548, 49122, 98272, 196574, 393180, 786394, 1572824, 3145686, 6291412, 12582866, 25165776, 50331598, 100663244, 201326538, 402653128, ...

MCS124240 : A₀ = 1; A_K+1 = 2 A_K + 2 K (score: 4)

2, 6, 16, 41, 102, 250, 608, 1473, 3562, 8606, 20784, 50185, 121166, 292530, 706240, 1705025, 4116306, 9937654, 23991632, 57920937, 139833526, 337588010, 815009568, 1967607169, 4750223930, ...

MCS1725568 : A₀ = 1; A₁ = 2; A_K+1 = 2 A_K + A_K-1 + K (score: 5)

2, 6, 16, 44, 120, 328, 896, 2448, 6688, 18272, 49920, 136384, 372608, 1017984, 2781184, 7598336, 20759040, 56714752, 154947584, 423324672, 1156544512, 3159738368, 8632565760, 23584608256, ...

MCS6738 (alias MCS862528) : A₀ = 0; A₁ = 1; A_N = 2 A_N-1 + 2 A_N-2 (score: 5)

Ratio A_n/A_n-1 converges on 1+sqrt(3) (A2605)

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

2, 6, 17, 49, 144, 428, 1279, 3831, 11486, 34450, 103341, 310013, 930028, 2790072, 8370203, 25110595, 75331770, 225995294, 677985865, 2033957577, 6101872712, 18305618116, 54916854327, ...

MCS249538 : A₀ = 2; A_K+1 = 3 A_K - K (score: 5)

2, -6, 17, -53, 156, -472, 1411, -4239, 12710, -38138, 114405, -343225, 1029664, -3089004, 9266999, -27801011, 83403018, -250209070, 750627193, -2251881597, 6755644772, -20266934336, 60800802987, ...

MCS999106 : A₀ = 2; A_K+1 = - 3 A_K - K (score: 5)

2, 6, 18, 48, 116, 262, 566, 1188, 2448, 4986, 10082, 20296, 40748, 81678, 163566, 327372, 655016, 1310338, 2621018, 5242416, 10485252, 20970966, 41942438, 83885428, 167771456, 335543562, ...

MCS248456 : A₀ = 1; A_K+1 = 2 A_K + K² + K (score: 5)

2, -6, 18, -54, 162, -486, 1458, -4374, 13122, -39366, 118098, -354294, 1062882, -3188646, 9565938, -28697814, 86093442, -258280326, 774840978, -2324522934, 6973568802, -20920706406, 62762119218, ...

MCS249730 : A₀ = 2; A_N = - 3 A_N-1 (score: 4)

2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098, 354294, 1062882, 3188646, 9565938, 28697814, 86093442, 258280326, 774840978, 2324522934, 6973568802, 20920706406, 62762119218, ...

MCS62338 : A₀ = 2; A_N = 3 A_N-1 (score: 4)

Powers of 3 times 2 (A8776)

2, 6, 18, 60, 210, 780, 3030, 12300, 51870, 226740, 1024050, 4768980, 22850610, 112466940, 567693030, 2934857100, 15520495710, 83868419220, 462626256930, ...

MCS26944 : A₀ = 0; A₁ = 1; A_K+1 = 2 A_K + K A_K-1 (score: 5)

2, 6, 18, 62, 258, 1302, 7826, 54798, 438402, 3945638, 39456402, 434020446, 5208245378, 67707189942, 947900659218, ...

MCS7786 (alias MCS249168) : A₀ = 0; A_K+1 = K A_K - A_K + 2 K (score: 5)

2, -6, 19, -55, 168, -500, 1505, -4509, 13534, -40594, 121791, -365363, 1096100, -3288288, 9864877, -29594617, 88783866, -266351582, 799054763, -2397164271, 7191492832, -21574478476, 64723435449, ...

MCS999042 : A₀ = 2; A_K+1 = - 3 A_K + K (score: 5)

2, 6, 19, 59, 180, 544, 1637, 4917, 14758, 44282, 132855, 398575, 1195736, 3587220, 10761673, 32285033, 96855114, 290565358, 871696091, 2615088291, 7845264892, 23535794696, 70607384109, ...

MCS249474 (alias MCS252832) : A₀ = 2; A_K+1 = 3 A_K + K (score: 5)

2, 6, 20, 58, 148, 346, 764, 1626, 3380, 6922, 14044, 28330, 56948, 114234, 228860, 458170, 916852, 1834282, 3669212, 7339146, 14679092, 29359066, 58719100, 117439258, 234879668, 469760586, ...

MCS124180 : A₀ = 1; A_K+1 = 2 A_K + 2 K² (score: 5)

2, 6, 20, 82, 412, 2474, 17320, 138562, 1247060, 12470602, 137176624, 1646119490, 21399553372, 299593747210, ...

MCS7848 : A₀ = 0; A_K+1 = K A_K + A_K + 2 (score: 5)

2, 6, 21, 43, 82, 134, 209, 303, 426, 574, 757, 971, 1226, 1518, 1857, 2239, 2674, 3158, 3701, 4299, 4962, 5686, 6481, 7343, 8282, 9294, 10389, 11563, 12826, 14174, 15617, 17151, 18786, 20518, ...

MCS31108 : A₀ = 1; A_K+1 = - A_K + K³ (score: 4)

2, 6, 21, 88, 445, 2676, 18739, 149920, 1349289, 13492900, 148421911, 1781062944, 23153818285, 324153456004, ...

MCS500880 : A₀ = 1; A_K+1 = K A_K + A_K + K + 1 (score: 5)

2, 6, 21, 91, 477, 2954, 21156, 172203, 1570984, 15882044, 176273469, 2131163673, 27881401219, 392470780740, ...

MCS6788 : A₀ = 0; A₁ = 1; A_K+1 = K A_K + A_K-1 + 1 (score: 5)

2, 6, 23, 110, 638, 4357, 34219, 303615, 3001932, 32717638, 389609725, 5032208788, 70061313308, ...

MCS3476742 : A₀ = 1; A₁ = 1; A_K+1 = K A_K - A_K-1 + 1 (score: 5)

2, 6, 23, 113, 672, 4681, 37335, 335343, 3348749, 36798904, 441251505, 5732920816, 80224092520, ...

MCS394337 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = K A_K - A_K-2 (score: 5)

2, -6, 24, -120, 720, -5040, 40320, -362880, 3628800, -39916800, 479001600, -6227020800, 87178291200, ...

MCS31128 : A₀ = 1; A_K+1 = - K A_K - A_K (score: 3)

2, -6, 24, -120, 720, -5040, 40320, -362880, 3628800, -39916800, 479001600, -6227020800, 87178291200, ...

MCS248625 : A₀ = -1; A_K+1 = - K A_K - 2 A_K (score: 5)

2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, ...

MCS30992 (alias MCS853030) : A₀ = 1; A_K+1 = K A_K + A_K (score: 3)

Factorials (A0142)

2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, ...

MCS62096 : A₀ = 1; A_K+1 = K A_K + 2 A_K (score: 4)

Factorials (A0142)

2, 6, 25, 127, 768, 5401, 43335, 390783, 3913231, 43088876, 517457295, 6730858066, 94275101800, ...

MCS394305 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = K A_K + A_K-2 (score: 5)

2, 6, 25, 130, 804, 5757, 46859, 427487, 4321728, 47966494, 579919655, 7586922008, 106796827766, ...

MCS3508486 : A₀ = 1; A₁ = 1; A_K+1 = K A_K + A_K-1 - 1 (score: 5)

2, 6, 26, 158, 1266, 12662, 151946, 2127246, 34035938, 612646886, 12252937722, 269564629886, ...

MCS7842 (alias MCS125480) : A₀ = 0; A_K+1 = 2 K A_K + 2 (score: 5)

2, -6, 32, -190, 1332, -10654, 95888, -958878, 10547660, -126571918, 1645434936, -23036089102, 345541336532, ...

MCS251288 (alias MCS853542) : A₀ = 1; A_K+1 = - K A_K - A_K + 2 (score: 5)

2, -7, 4, -14, 12, -26, 29, -53, 66, -109, 147, -229, 321, -486, 696, -1037, 1502, -2220, 3234, -4760, 6955, -10215, 14948, -21931, 32117, -47095, 68995, -101144, 148206, -217235, 318344, -466586, ...

MCS814129 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = - A_K - A_K-2 - K (score: 5)

2, -7, 6, -27, 30, -95, 142, -347, 614, -1327, 2534, -5211, 10254, -20703, 41182, -82619, 164950, -330223, 660086, -1320571, 2640702, -5281887, 10563246, -21127067, 42253510, -84507695, 169014662, ...

MCS501132 : A₀ = 1; A_K+1 = - 2 A_K - K² + 1 (score: 5)

2, 7, -6, -37, 48, 303, -424, -3021, 4674, 36263, -60750, -507669, 911264, 8122719, -15491472, -146208925, 294337986, 2924178519, -6181097686, -64331927397, 142165246800, ...

MCS109697 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 + K - 1 (score: 5)

2, -7, 7, -16, 21, -39, 58, -99, 155, -256, 409, -667, 1074, -1743, 2815, -4560, 7373, -11935, 19306, -31243, 50547, -81792, 132337, -214131, 346466, -560599, 907063, -1467664, 2374725, -3842391, ...

MCS13676 : A₀ = 0; A₁ = 1; A_N = - A_N-1 + A_N-2 - 2 (score: 5)

2, 7, -10, -47, 82, 425, -818, -4673, 9818, 60751, -137450, -911263, 2199202, 15491473, -39585634, -294337985, 791712682, 6181097687, -17417679002, -142165246799, 418024296050, ...

MCS1744950 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K-1 + 2 (score: 5)

2, 7, 12, 11, 12, 27, 40, 27, 20, 67, 104, 35, -12, 155, 280, -21, -236, 403, 872, -365, -1260, 1259, 3096, -1893, -5516, 4515, 11816, -8189, -22732, 17339, 46488, -33589, -91820, 68403, 184936, ...

MCS13356 : A₀ = 0; A₁ = 1; A_K+1 = - 2 A_K-1 + K² (score: 5)

2, 7, 12, 21, 30, 43, 56, 73, 90, 111, 132, 157, 182, 211, 240, 273, 306, 343, 380, 421, 462, 507, 552, 601, 650, 703, 756, 813, 870, 931, 992, 1057, 1122, 1191, 1260, 1333, 1406, 1483, 1560, ...

MCS31330 : A₀ = 0; A_K+1 = - A_K + 2 K² + 1 (score: 5)

2, 7, 14, 23, 34, 47, 62, 79, 98, 119, 142, 167, 194, 223, 254, 287, 322, 359, 398, 439, 482, 527, 574, 623, 674, 727, 782, 839, 898, 959, 1022, 1087, 1154, 1223, 1294, 1367, 1442, 1519, 1598, ...

MCS7084 (alias MCS14186, MCS28374, MCS504993)

A_K = K² - 2 (score: 4)

2, 7, 14, 27, 44, 69, 100, 141, 190, 251, 322, 407, 504, 617, 744, 889, 1050, 1231, 1430, 1651, 1892, 2157, 2444, 2757, 3094, 3459, 3850, 4271, 4720, 5201, 5712, 6257, 6834, 7447, 8094, 8779, ...

MCS13384 : A₀ = 0; A₁ = 1; A_K+1 = A_K-1 + K² + K (score: 5)

2, 7, 14, 47, 104, 383, 944, 3839, 10394, 46079, 135134, 645119, 2027024, 10321919, 34459424, 185794559, 654729074, 3715891199, 13749310574, 81749606399, 316234143224, ...

MCS877577 : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 + K - 1 (score: 5)

2, 7, 14, 47, 104, 383, 944, 3839, 10394, 46079, 135134, 645119, 2027024, 10321919, 34459424, 185794559, 654729074, 3715891199, 13749310574, 81749606399, 316234143224, ...

MCS856585 : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 + A_K-1 + K (score: 5)

2, 7, 15, 26, 40, 57, 77, 100, 126, 155, 187, 222, 260, 301, 345, 392, 442, 495, 551, 610, 672, 737, 805, 876, 950, 1027, 1107, 1190, 1276, 1365, 1457, 1552, 1650, 1751, 1855, 1962, 2072, 2185, ...

MCS252528 : A₀ = 1; A_K+1 = A_K + 3 K - 1 (score: 5)

2, 7, 16, 25, 34, 47, 64, 81, 98, 119, 144, 169, 194, 223, 256, 289, 322, 359, 400, 441, 482, 527, 576, 625, 674, 727, 784, 841, 898, 959, 1024, 1089, 1154, 1223, 1296, 1369, 1442, 1519, 1600, ...

MCS13362 : A₀ = 0; A₁ = 1; A_K+1 = - A_K-1 + 2 K² (score: 5)

2, 7, 16, 29, 46, 67, 92, 121, 154, 191, 232, 277, 326, 379, 436, 497, 562, 631, 704, 781, 862, 947, 1036, 1129, 1226, 1327, 1432, 1541, 1654, 1771, 1892, 2017, 2146, 2279, 2416, 2557, 2702, 2851, ...

MCS28314 : A_K = 2 K² - K + 1 (score: 5)

2, 7, -16, -49, 104, 383, -946, -3841, 10394, 46079, -135136, -645121, 2027024, 10321919, -34459426, -185794561, 654729074, 3715891199, -13749310576, -81749606401, 316234143224, ...

MCS878093 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K-1 - K - 1 (score: 5)

2, 7, 17, 34, 60, 97, 147, 212, 294, 395, 517, 662, 832, 1029, 1255, 1512, 1802, 2127, 2489, 2890, 3332, 3817, 4347, 4924, 5550, 6227, 6957, 7742, 8584, 9485, 10447, 11472, 12562, 13719, 14945, ...

MCS250385 : A₀ = -1; A_K+1 = A_K + K² + 1 (score: 5)

2, 7, 18, 41, 84, 161, 294, 519, 894, 1513, 2528, 4185, 6882, 11263, 18370, 29889, 48548, 78761, 127670, 206831, 334942, 542257, 877728, 1420561, 2298914, 3720151, 6019794, 9740729, 15761364, ...

MCS13448 : A₀ = 0; A₁ = 1; A_K+1 = A_K + A_K-1 + K² (score: 5)

2, 7, 18, 41, 88, 183, 374, 757, 1524, 3059, 6130, 12273, 24560, 49135, 98286, 196589, 393196, 786411, 1572842, 3145705, 6291432, 12582887, 25165798, 50331621, 100663268, 201326563, 402653154, ...

MCS7850 : A₀ = 0; A_K+1 = 2 A_K + K + 2 (score: 5)

2, -7, 19, -50, 131, -343, 898, -2351, 6155, -16114, 42187, -110447, 289154, -757015, 1981891, -5188658, 13584083, -35563591, 93106690, -243756479, 638162747, -1670731762, 4374032539, ...

MCS1735872 : A₀ = 1; A₁ = 2; A_N = - 3 A_N-1 - A_N-2 (score: 5)

Horadam sequence W_n(1, 2; -1, -3)

2, 7, 20, 49, 110, 235, 488, 997, 2018, 4063, 8156, 16345, 32726, 65491, 131024, 262093, 524234, 1048519, 2097092, 4194241, 8388542, 16777147, 33554360, 67108789, 134217650, 268435375, 536870828, ...

MCS124272 : A₀ = 1; A_K+1 = 2 A_K + 3 K (score: 5)

2, -7, 20, -61, 182, -547, 1640, -4921, 14762, -44287, 132860, -398581, 1195742, -3587227, 10761680, -32285041, 96855122, -290565367, 871696100, -2615088301, 7845264902, -23535794707, 70607384120, ...

MCS3951 (alias MCS505793, MCS1011586) : A₀ = 0; A_N = - 3 A_N-1 - 1 (score: 4)

2, 7, 20, 61, 182, 547, 1640, 4921, 14762, 44287, 132860, 398581, 1195742, 3587227, 10761680, 32285041, 96855122, 290565367, 871696100, 2615088301, 7845264902, 23535794707, 70607384120, ...

MCS6739 : A₀ = 0; A₁ = 1; A_N = 2 A_N-1 + 3 A_N-2 (score: 6)

A15518

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

2, 7, 21, 44, 82, 135, 209, 304, 426, 575, 757, 972, 1226, 1519, 1857, 2240, 2674, 3159, 3701, 4300, 4962, 5687, 6481, 7344, 8282, 9295, 10389, 11564, 12826, 14175, 15617, 17152, 18786, 20519, ...

MCS125316 : A₀ = 1; A_K+1 = - A_K + K³ + 1 (score: 5)

2, 7, 22, 59, 142, 319, 686, 1435, 2950, 5999, 12118, 24379, 48926, 98047, 196318, 392891, 786070, 1572463, 3145286, 6290971, 12582382, 25165247, 50331022, 100662619, 201325862, 402652399, ...

MCS252552 : A₀ = 1; A_K+1 = 2 A_K + K² - 1 (score: 5)

2, 7, 22, 67, 202, 607, 1822, 5467, 16402, 49207, 147622, 442867, 1328602, 3985807, 11957422, 35872267, 107616802, 322850407, 968551222, 2905653667, 8716961002, 26150883007, 78452649022, ...

MCS250754 : A₀ = 2; A_N = 3 A_N-1 + 1 (score: 5)

2, 7, 23, 76, 251, 829, 2738, 9043, 29867, 98644, 325799, 1076041, 3553922, 11737807, 38767343, 128039836, 422886851, 1396700389, 4612988018, 15235664443, 50319981347, 166195608484, 548906806799, ...

MCS433280 : A₀ = 1; A₁ = 2; A_N = 3 A_N-1 + A_N-2 (score: 5)

Horadam sequence W_n(1, 2; 1, 3)

2, 7, 26, 115, 606, 3757, 26912, 219061, 1998470, 20203771, 224239962, 2711083327, 35468323226, 499267608505, ...

MCS6692 : A₀ = 0; A₁ = 1; A_K+1 = K A_K + A_K-1 + K (score: 5)

2, 7, 29, 147, 889, 6252, 50163, 452356, 4529812, 49878095, 598989496, 7791393260, 109129383735, ...

MCS197153 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = K A_K + A_K-2 (score: 5)

2, 7, 30, 153, 922, 6459, 51678, 465109, 4651098, 51162087, 613945054, 7981285713, 111737999994, ...

MCS248464 : A₀ = 1; A_K+1 = K A_K + 2 A_K + K (score: 5)

2, -7, 30, -157, 972, -6961, 56660, -516901, 5225670, -57999271, 701216922, -9173819257, 129134686520, ...

MCS427201 : A₀ = -1; A₁ = 0; A_K+1 = - K A_K + A_K-1 (score: 5)

2, 7, 30, 157, 972, 6961, 56660, 516901, 5225670, 57999271, 701216922, 9173819257, 129134686520, ...

MCS6756 : A₀ = 0; A₁ = 1; A_K+1 = K A_K - A_K + A_K-1 (score: 5)

2, 7, 30, 157, 972, 6961, 56660, 516901, 5225670, 57999271, 701216922, 9173819257, 129134686520, ...

MCS3417110 : A₀ = 1; A₁ = 0; A_K+1 = K A_K + A_K-1 (score: 5)

2, 7, 30, 157, 972, 6961, 56660, 516901, 5225670, 57999271, 701216922, 9173819257, 129134686520, ...

MCS6724 : A₀ = 0; A₁ = 1; A_K+1 = K A_K + A_K + A_K-1 (score: 5)

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