Minimally Complex Sequences  


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2, 5, 9, 16, 27, 45, 74, 121, 197, 320, 519, 841, 1362, 2205, 3569, 5776, 9347, 15125, 24474, 39601, 64077, 103680, 167759, 271441, 439202, 710645, 1149849, 1860496, 3010347, 4870845, 7881194, ...

MCS1747072 : A0 = 1; A1 = 2; AN = AN-1 + AN-2 + 2 (score: 5)

2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, ...

MCS787220 : A0 = 1; A1 = 2; A2 = 5; AN = - AN-3 (score: 5)

2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, 2, 5, -2, -5, ...

MCS1710122 : A0 = 2; A1 = 5; AN = - AN-2 (score: 5)

Horadam sequence Wn(2, 5; -1, 0)

2, 5, -5, 0, 16, -9, -15, 42, -2, -71, 87, 68, -228, 107, 365, -562, -150, 1293, -973, -1592, 3560, -353, -6743, 7474, 6038, -20959, 8911, 33036, -50828, -15213, 116901, -86442, -147326, 320245, ...

MCS13847302 : A0 = 1; A1 = 1; AK+1 = - AK - 2 AK-1 + K (score: 5)

2, 5, 10, 15, 20, 27, 36, 45, 54, 65, 78, 91, 104, 119, 136, 153, 170, 189, 210, 231, 252, 275, 300, 325, 350, 377, 406, 435, 464, 495, 528, 561, 594, 629, 666, 703, 740, 779, 820, 861, 902, 945, ...

MCS13388 : A0 = 0; A1 = 1; AK+1 = - AK-1 + K2 + K (score: 5)

2, 5, 10, 17, 26, 37, 50, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 325, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 1025, 1090, 1157, 1226, 1297, 1370, 1445, 1522, ...

MCS1768 (alias MCS250448) : AK = K2 + 1 (score: 3)

Squares plus one (A2522)

2, 5, 10, 18, 30, 46, 67, 94, 127, 167, 215, 271, 336, 411, 496, 592, 700, 820, 953, 1100, 1261, 1437, 1629, 1837, 2062, 2305, 2566, 2846, 3146, 3466, 3807, 4170, 4555, 4963, 5395, 5851, 6332, ...

MCS1575174 : A0 = 1; A1 = 1; A2 = 2; AK+1 = AK-2 + K2 (score: 5)

2, 5, 10, 19, 34, 59, 100, 167, 276, 453, 740, 1205, 1958, 3177, 5150, 8343, 13510, 21871, 35400, 57291, 92712, 150025, 242760, 392809, 635594, 1028429, 1664050, 2692507, 4356586, 7049123, ...

MCS3364 (alias MCS3482752) : A0 = 0; A1 = 1; AK+1 = AK + AK-1 + K (score: 4)

2, 5, 10, 19, 36, 69, 134, 263, 520, 1033, 2058, 4107, 8204, 16397, 32782, 65551, 131088, 262161, 524306, 1048595, 2097172, 4194325, 8388630, 16777239, 33554456, 67108889, 134217754, 268435483, ...

MCS15701 (alias MCS1002178) : A0 = 0; AK+1 = 2 AK - K + 2 (score: 5)

2, 5, 10, 21, 42, 85, 170, 341, 682, 1365, 2730, 5461, 10922, 21845, 43690, 87381, 174762, 349525, 699050, 1398101, 2796202, 5592405, 11184810, 22369621, 44739242, 89478485, 178956970, 357913941, ...

MCS13602 (alias MCS1741120, MCS1741121) : A0 = 0; A1 = 1; AN = AN-1 + 2 AN-2 + 1 (score: 5)

2, 5, 10, 25, 56, 157, 400, 1265, 3610, 12661, 39722, 151945, 516400, 2127245, 7746016, 34035937, 131682290, 612646885, 2501963530, 12252937721, 52541234152, 269564629885, ...

MCS54336 : A0 = 0; A1 = 1; AK+1 = K AK-1 + K + 1 (score: 5)

2, 5, 10, 25, 56, 157, 400, 1265, 3610, 12661, 39722, 151945, 516400, 2127245, 7746016, 34035937, 131682290, 612646885, 2501963530, 12252937721, 52541234152, 269564629885, ...

MCS856841 : A0 = 0; A1 = 0; AK+1 = K AK-1 - AK-1 + K (score: 5)

2, 5, 11, 21, 36, 57, 85, 121, 166, 221, 287, 365, 456, 561, 681, 817, 970, 1141, 1331, 1541, 1772, 2025, 2301, 2601, 2926, 3277, 3655, 4061, 4496, 4961, 5457, 5985, 6546, 7141, 7771, 8437, 9140, ...

MCS854150 (alias MCS6902534) : A0 = 1; A1 = 1; AK+1 = AK-1 + K2 (score: 4)

2, 5, 11, 21, 38, 66, 112, 187, 309, 507, 828, 1348, 2190, 3553, 5759, 9329, 15106, 24454, 39580, 64055, 103657, 167735, 271416, 439176, 710618, 1149821, 1860467, 3010317, 4870814, 7881162, ...

MCS1722625 (alias MCS3482753) : A0 = -1; A1 = 0; AK+1 = AK + AK-1 + K (score: 5)

2, 5, 11, 22, 40, 67, 105, 156, 222, 305, 407, 530, 676, 847, 1045, 1272, 1530, 1821, 2147, 2510, 2912, 3355, 3841, 4372, 4950, 5577, 6255, 6986, 7772, 8615, 9517, 10480, 11506, 12597, 13755, ...

MCS15696 : A0 = 0; AK+1 = AK + K2 + 2 (score: 5)

2, 5, 11, 22, 41, 73, 126, 213, 355, 586, 961, 1569, 2554, 4149, 6731, 10910, 17673, 28617, 46326, 74981, 121347, 196370, 317761, 514177, 831986, 1346213, 2178251, 3524518, 5702825, 9227401, ...

MCS1723008 : A0 = 1; A1 = 2; AK+1 = AK + AK-1 + 2 K (score: 5)

2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, 3145727, 6291455, 12582911, 25165823, 50331647, 100663295, 201326591, 402653183, ...

MCS250498 : A0 = 2; AN = 2 AN-1 + 1 (score: 4)

2, 5, 11, 24, 50, 103, 209, 422, 848, 1701, 3407, 6820, 13646, 27299, 54605, 109218, 218444, 436897, 873803, 1747616, 3495242, 6990495, 13981001, 27962014, 55924040, 111848093, 223696199, ...

MCS1722688 : A0 = 1; A1 = 2; AK+1 = AK + 2 AK-1 + K (score: 5)

2, 5, 11, 24, 53, 117, 258, 569, 1255, 2768, 6105, 13465, 29698, 65501, 144467, 318632, 702765, 1549997, 3418626, 7540017, 16630031, 36678688, 80897393, 178424817, 393528322, 867954037, ...

MCS403489 (alias MCS3227910) : A0 = 0; A1 = 1; A2 = 1; AN = 2 AN-1 + AN-3 (score: 5)

2, 5, 11, 26, 59, 137, 314, 725, 1667, 3842, 8843, 20369, 46898, 108005, 248699, 572714, 1318811, 3036953, 6993386, 16104245, 37084403, 85397138, 196650347, 452841761, 1042792802, 2401318085, ...

MCS430528 : A0 = 1; A1 = 2; AN = AN-1 + 3 AN-2 (score: 5)

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

2, 5, 12, 19, 30, 41, 56, 71, 90, 109, 132, 155, 182, 209, 240, 271, 306, 341, 380, 419, 462, 505, 552, 599, 650, 701, 756, 811, 870, 929, 992, 1055, 1122, 1189, 1260, 1331, 1406, 1481, 1560, ...

MCS31586 : A0 = 0; AK+1 = - AK + 2 K2 - 1 (score: 5)

2, 5, 12, 22, 38, 59, 88, 124, 170, 225, 292, 370, 462, 567, 688, 824, 978, 1149, 1340, 1550, 1782, 2035, 2312, 2612, 2938, 3289, 3668, 4074, 4510, 4975, 5472, 6000, 6562, 7157, 7788, 8454, 9158, ...

MCS868897 : A0 = 0; A1 = 0; AK+1 = AK-1 + K2 + 1 (score: 5)

2, 5, 12, 23, 36, 49, 62, 77, 96, 119, 144, 169, 194, 221, 252, 287, 324, 361, 398, 437, 480, 527, 576, 625, 674, 725, 780, 839, 900, 961, 1022, 1085, 1152, 1223, 1296, 1369, 1442, 1517, 1596, ...

MCS13452 : A0 = 0; A1 = 1; AK+1 = AK - AK-1 + K2 (score: 5)

2, 5, 12, 25, 46, 77, 120, 177, 250, 341, 452, 585, 742, 925, 1136, 1377, 1650, 1957, 2300, 2681, 3102, 3565, 4072, 4625, 5226, 5877, 6580, 7337, 8150, 9021, 9952, 10945, 12002, 13125, 14316, ...

MCS31308 (alias MCS500872) : A0 = 0; AK+1 = AK + K2 - K + 1 (score: 5)

2, 5, 12, 27, 58, 121, 248, 503, 1014, 2037, 4084, 8179, 16370, 32753, 65520, 131055, 262126, 524269, 1048556, 2097131, 4194282, 8388585, 16777192, 33554407, 67108838, 134217701, 268435428, ...

MCS62112 (alias MCS252576, MCS1002114) : A0 = 1; AK+1 = 2 AK + K (score: 3)

2N-N (A0325)

2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109, 15994428, 38613965, 93222358, 225058681, 543339720, 1311738121, 3166815962, 7645370045, ...

MCS1684 (alias MCS431232, MCS6899734) : A0 = 0; A1 = 1; AN = 2 AN-1 + AN-2 (score: 4)

Pell Numbers (A0129)

Horadam sequence Wn(0, 1; 1, 2), Lucas sequence Un(2, -1) ; Horadam sequence Wn(1, 2; 1, 2) ; Horadam sequence Wn(1, 0; 1, 2)

2, 5, 12, 33, 94, 293, 952, 3297, 11866, 44837, 175364, 713409, 2993142, 12980869, 57878000, 265571905, 1249497906, 6029792197, 29770252412, 150366096353, 775541397006, ...

MCS54400 : A0 = 0; A1 = 1; AK+1 = AK + K AK-1 + 1 (score: 5)

2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229, 1346269, 3524578, 9227465, 24157817, 63245986, 165580141, 433494437, 1134903170, 2971215073, 7778742049, 20365011074, ...

MCS433344 (alias MCS1733382) : A0 = 1; A1 = 2; AN = 3 AN-1 - AN-2 (score: 5)

Odd-numbered Fibonacci numbers (A1519)

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

2, 5, 14, 33, 66, 117, 190, 289, 418, 581, 782, 1025, 1314, 1653, 2046, 2497, 3010, 3589, 4238, 4961, 5762, 6645, 7614, 8673, 9826, 11077, 12430, 13889, 15458, 17141, 18942, 20865, 22914, 25093, ...

MCS250388 : A0 = 1; AK+1 = AK + 2 K2 + 1 (score: 5)

2, 5, 14, 37, 90, 205, 446, 941, 1946, 3973, 8046, 16213, 32570, 65309, 130814, 261853, 523962, 1048213, 2096750, 4193861, 8388122, 16776685, 33553854, 67108237, 134217050, 268434725, 536870126, ...

MCS62088 : A0 = 1; AK+1 = 2 AK + K2 (score: 4)

2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734, 1743392201, 5230176602, 15690529805, 47071589414, 141214768241, ...

MCS63200 (alias MCS252802) : A0 = 1; AN = 3 AN-1 - 1 (score: 4)

2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355, 11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197, 199037675054, ...

MCS431112 : A0 = 1; A1 = 2; AK+1 = 2 AK + K AK-1 (score: 5)

2, 5, 14, 47, 194, 977, 5870, 41099, 328802, 2959229, 29592302, 325515335, 3906184034, 50780392457, 710925494414, ...

MCS7844 (alias MCS251024) : A0 = 0; AK+1 = K AK + K + 2 (score: 5)

2, 5, 14, 47, 194, 977, 5870, 41099, 328802, 2959229, 29592302, 325515335, 3906184034, 50780392457, 710925494414, ...

MCS15668 (alias MCS501392) : A0 = 0; AK+1 = K AK - AK + K + 1 (score: 5)

2, 5, 14, 47, 194, 977, 5870, 41099, 328802, 2959229, 29592302, 325515335, 3906184034, 50780392457, 710925494414, ...

MCS15540 : A0 = 0; AK+1 = K AK - 2 AK + K (score: 5)

2, 5, 16, 63, 304, 1767, 12072, 94817, 841290, 8318093, 90657744, 1079574847, 13943815280, 194133839087, ...

MCS6694 : A0 = 0; A1 = 1; AK+1 = K AK - AK-1 + K (score: 5)

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

MCS976 (alias MCS3916, MCS31248, MCS62497, MCS125328)

A0 = 0; AK+1 = K AK + 1 (score: 3)

Distinct Ordered Subsets of Set with N Elements (A0522)

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

MCS125200 : A0 = 1; AK+1 = K AK + AK + 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; AK+1 = K AK - 2 AK + 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; AK+1 = K AK + AK-2 (score: 5)

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

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

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

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

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

MCS3459334 : A0 = 1; A1 = 1; AK+1 = K AK - AK + AK-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; AK+1 = 2 AK + K3 (score: 5)

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

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

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

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

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

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

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

MCS15654 : A0 = 0; AK+1 = K AK + AK - 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; AK+1 = K AK - AK-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; AK+1 = - AK + K3 - 1 (score: 5)

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

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

Horadam sequence Wn(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; AK+1 = - 2 AK-1 + 2 K (score: 5)

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; AK+1 = - K AK-1 + K2 (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; AK+1 = - AK + K2 - 1 (score: 4)

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; AK+1 = AK - K AK-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; AN = - 2 AN-2 - 2 (score: 5)

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; AK+1 = AK - AK-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; AK+1 = - AK-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; AK+1 = 2 AK-1 + 2 K (score: 5)

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; AK+1 = 3 AK-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; AK+1 = AK + 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)

AK = 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; AK+1 = AK-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; AK+1 = K AK-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; AK+1 = K AK-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; AK+1 = AK + 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; AK+1 = AK + AK-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; AK+1 = AK + 2 AK-1 + K (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; AK+1 = AK-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; AK+1 = AK + AK-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; AN = 2 AN-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; AK+1 = AK + 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; AK+1 = K AK-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; AN = 2 AN-1 + AN-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; AK+1 = K AK-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; AN = 2 AN-1 + 2 AN-2 - AN-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; AK+1 = AK + K AK-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; AK+1 = AK + K AK-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; AK+1 = 2 AK + 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; AK+1 = 2 AK + AK-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; AN = 2 AN-1 + 2 AN-2 (score: 5)

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

Horadam sequence Wn(0, 1; 2, 2), Lucas sequence Un(2, -2) ; Horadam sequence Wn(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; AK+1 = 3 AK - 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; AK+1 = 2 AK + 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, ...

MCS62338 : A0 = 2; AN = 3 AN-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; AK+1 = 2 AK + K AK-1 (score: 5)

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

MCS7786 (alias MCS249168) : A0 = 0; AK+1 = K AK - AK + 2 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; AK+1 = 3 AK + 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; AK+1 = 2 AK + 2 K2 (score: 5)

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

MCS7848 : A0 = 0; AK+1 = K AK + AK + 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; AK+1 = - AK + K3 (score: 4)

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

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

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

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

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

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

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

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

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

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

Factorials (A0142)

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

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

Factorials (A0142)

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

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

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

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

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

MCS7842 (alias MCS125480) : A0 = 0; AK+1 = 2 K AK + 2 (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; AK+1 = - K AK-1 + K - 1 (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; AK+1 = - 2 AK-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; AK+1 = - AK + 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)

AK = 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; AK+1 = AK-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; AK+1 = K AK-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; AK+1 = K AK-1 + AK-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; AK+1 = AK + 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; AK+1 = - AK-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 : AK = 2 K2 - 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; AK+1 = AK + 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; AK+1 = AK + AK-1 + K2 (score: 5)


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