Munafo's Classical Sequences

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2, 3, 7, 13, 36, 79, 253, 633, 2278, 6331, 25059, 75973, 325768, 1063623, 4886521, 17017969, 83070858, 306323443, 1578346303, 6126468861, 33145272364, 134782314943, 762341264373, ...

MCS868390 (alias MCS54320, MCS868872, MCS3476518)

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

2, 3, 7, 14, 38, 91, 280, 766, 2611, 7940, 29487, 97891, 391271, 1399961, 5966956, 22790647, 102838213, 416198602, 1976716694, 8426810253, 41927249176, 187366542260, 972753541301, ...

MCS1574022 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = K A_K-1 + A_K-2 (score: 5)

2, 3, 7, 16, 35, 77, 170, 375, 827, 1824, 4023, 8873, 19570, 43163, 95199, 209968, 463099, 1021397, 2252762, 4968623, 10958643, 24170048, 53308719, 117576081, 259322210, 571953139, 1261482359, ...

MCS806976 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = 2 A_N-1 + A_N-3 (score: 5)

2, 3, 7, 16, 44, 124, 388, 1256, 4360, 15664, 59264, 231568, 942736, 3953120, 17151424, 76448224, 350871008, 1650490816, 7966168960, 39325494464, 198648873664, ...

MCS215048 : A₀ = 1; A₁ = 2; A_K+1 = A_K + K A_K-1 (score: 4)

2, 3, 7, 22, 89, 446, 2677, 18740, 149921, 1349290, 13492901, 148421912, 1781062945, 23153818286, 324153456005, ...

MCS500802 : A₀ = 2; A_K+1 = K A_K + A_K + 1 (score: 5)

2, 3, 7, 23, 95, 482, 2915, 20500, 164482, 1483253, 14853030, 163547812, 1964056997, 25547593991, 357829863686, ...

MCS394304 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = K A_K + A_K-2 (score: 5)

2, 3, 7, 25, 118, 683, 4663, 36621, 324926, 3212639, 35014103, 416956597, 5385421658, 74978946615, ...

MCS860992 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + A_K - A_K-1 (score: 5)

2, 3, 8, 11, 18, 23, 32, 39, 50, 59, 72, 83, 98, 111, 128, 143, 162, 179, 200, 219, 242, 263, 288, 311, 338, 363, 392, 419, 450, 479, 512, 543, 578, 611, 648, 683, 722, 759, 800, 839, 882, 923, ...

MCS1714693 : A₀ = 0; A₁ = -1; A_K+1 = A_K-1 + 2 K (score: 5)

2, 3, 8, 11, 22, 29, 52, 67, 114, 145, 240, 303, 494, 621, 1004, 1259, 2026, 2537, 4072, 5095, 8166, 10213, 16356, 20451, 32738, 40929, 65504, 81887, 131038, 163805, 262108, 327643, 524250, ...

MCS1739073 : A₀ = 0; A₁ = 0; A_K+1 = 2 A_K-1 + K + 1 (score: 5)

2, 3, 8, 14, 22, 28, 35, 42, 53, 65, 79, 91, 104, 117, 134, 152, 172, 190, 209, 228, 251, 275, 301, 325, 350, 375, 404, 434, 466, 496, 527, 558, 593, 629, 667, 703, 740, 777, 818, 860, 904, 946, ...

MCS1575302 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - A_K-2 + K² (score: 5)

2, 3, 8, 15, 28, 45, 70, 101, 142, 191, 252, 323, 408, 505, 618, 745, 890, 1051, 1232, 1431, 1652, 1893, 2158, 2445, 2758, 3095, 3460, 3851, 4272, 4721, 5202, 5713, 6258, 6835, 7448, 8095, 8780, ...

MCS856608 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 + K² + K (score: 5)

2, 3, 8, 15, 32, 55, 100, 159, 264, 399, 628, 919, 1400, 2007, 2996, 4239, 6248, 8767, 12820, 17895, 26040, 36231, 52564, 72991, 105704, 146607, 212084, 293943, 424952, 588727, 850804, 1178415, ...

MCS427296 : A₀ = 1; A₁ = 2; A_K+1 = 2 A_K-1 + K² (score: 5)

2, 3, 8, 15, 40, 85, 252, 609, 2032, 5499, 20340, 60511, 244104, 786669, 3417484, 11800065, 54679776, 200601139, 984236004, 3811421679, 19684720120, 80039855301, 433063842684, ...

MCS428552 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 + 2 K (score: 5)

2, 3, 8, 15, 44, 95, 314, 767, 2834, 7679, 31184, 92159, 405404, 1290239, 6081074, 20643839, 103378274, 371589119, 1964187224, 7431782399, 41247931724, 163499212799, 948702429674, ...

MCS856584 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 + A_K-1 + K (score: 5)

2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 2027025, 10321920, 34459425, 185794560, 654729075, 3715891200, 13749310575, 81749606400, 316234143225, ...

MCS213030 (alias MCS427272, MCS854054) : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 (score: 3)

Semifactorials or ''double'' factorials (A006882)

2, 3, 8, 19, 46, 111, 268, 647, 1562, 3771, 9104, 21979, 53062, 128103, 309268, 746639, 1802546, 4351731, 10506008, 25363747, 61233502, 147830751, 356895004, 861620759, 2080136522, 5021893803, ...

MCS1724930 : A₀ = 2; A₁ = 3; A_N = 2 A_N-1 + A_N-2 (score: 5)

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

2, 3, 8, 27, 116, 607, 3758, 26913, 219062, 1998471, 20203772, 224239963, 2711083328, 35468323227, 499267608506, ...

MCS213568 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + A_K-1 (score: 4)

2, 3, 8, 30, 147, 874, 6088, 48557, 436139, 4355302, 47859765, 573881041, 7456098231, 104337515469, ...

MCS1577350 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = K A_K - A_K-2 (score: 5)

2, 3, 9, 16, 60, 119, 524, 1130, 5645, 13036, 72255, 176859, 1070789, 2757489, 18026554, 48564013, 339747037, 953253706, 7086123764, 20631834495, 162027592866, 488077904116, ...

MCS6298166 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = K A_K-1 - A_K-2 (score: 5)

2, 3, 9, 17, 62, 135, 557, 1349, 6126, 16187, 79637, 226617, 1194554, 3625871, 20307417, 65265677, 385840922, 1305313539, 8102659361, 28716897857, 186361165302, 689205548567, ...

MCS3508262 : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 + A_K-1 - 1 (score: 5)

2, 3, 9, 19, 73, 191, 877, 2675, 14033, 48151, 280661, 1059323, 6735865, 27542399, 188604221, 826271971, 6035335073, 28093247015, 217272062629, ...

MCS434196 : A₀ = 1; A₁ = 2; A_K+1 = 2 K A_K-1 + 1 (score: 5)

2, 3, 10, 17, 56, 109, 400, 881, 3610, 8821, 39722, 105865, 516400, 1482125, 7746016, 23714017, 131682290, 426852325, 2501963530, 8537046521, 52541234152, 187815023485, ...

MCS869385 : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 + K + 1 (score: 5)

2, 3, 10, 21, 42, 71, 114, 169, 242, 331, 442, 573, 730, 911, 1122, 1361, 1634, 1939, 2282, 2661, 3082, 3543, 4050, 4601, 5202, 5851, 6554, 7309, 8122, 8991, 9922, 10913, 11970, 13091, 14282, ...

MCS427088 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 + 2 K² (score: 5)

2, 3, 10, 21, 84, 215, 1014, 3017, 16232, 54315, 324650, 1194941, 7791612, 31068479, 218165150, 932054385, 6981284816, 31689849107, 251326253394, ...

MCS428052 : A₀ = 1; A₁ = 2; A_K+1 = 2 K A_K-1 + K (score: 5)

2, 3, 10, 21, 90, 231, 1170, 3465, 19890, 65835, 417690, 1514205, 10442250, 40883535, 302825250, 1267389585, 9993233250, 44358635475, 369749630250, ...

MCS427028 : A₀ = 1; A₁ = 2; A_K+1 = 2 K A_K-1 + A_K-1 (score: 5)

2, 3, 10, 29, 66, 127, 218, 345, 514, 731, 1002, 1333, 1730, 2199, 2746, 3377, 4098, 4915, 5834, 6861, 8002, 9263, 10650, 12169, 13826, 15627, 17578, 19685, 21954, 24391, 27002, 29793, 32770, ...

MCS7080 : A_K = K³ + 2 (score: 5)

2, 3, 10, 39, 196, 1175, 8226, 65807, 592264, 5922639, 65149030, 781788359, 10163248668, 142285481351, ...

MCS213256 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + K A_K-1 (score: 5)

2, 3, 10, 57, 446, 4403, 52390, 729057, 11612522, 208296339, 4154314258, 91186617337, ...

MCS427680 : A₀ = 1; A₁ = 2; A_K+1 = 2 K A_K - A_K-1 (score: 5)

2, 3, 12, 20, 78, 147, 632, 1332, 6330, 14663, 75972, 190632, 1063622, 2859495, 17017968, 48611432, 306323442, 923617227, 6126468860, 19395961788, 134782314942, 446107121147, ...

MCS428049 : A₀ = -1; A₁ = 0; A_K+1 = K A_K-1 + K (score: 5)

2, 3, 12, 25, 138, 343, 2200, 6165, 43990, 135619, 1055748, 3526081, 29560930, 105782415, 945949744, 3596602093, 34054190766, 136670879515, ...

MCS1716310 : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K-1 - K (score: 5)

2, 3, 12, 27, 144, 405, 2592, 8505, 62208, 229635, 1866240, 7577955, 67184640, 295540245, 2821754880, 13299311025, 135444234240, 678264862275, ...

MCS106524 : A₀ = 1; A₁ = 2; A_K+1 = 3 K A_K-1 (score: 5)

2, 3, 12, 39, 120, 355, 1034, 2991, 8628, 24861, 71604, 206197, 593744, 1709643, 4922748, 14174517, 40813926, 117519049, 338382650, 974334045, 2805483108, 8078066697, 23259866070, 66974115127, ...

MCS26595424 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = 3 A_K - A_K-2 + K + 2 (score: 9)

Not (3^N-3)/2 (see MCS1979)

2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, ...

MCS196740 : A₀ = 0; A₁ = 2; A₂ = 4; A_N = A_N-3 (score: 5)

2, 4, 1, 0, 4, 6, 3, 2, 6, 8, 5, 4, 8, 10, 7, 6, 10, 12, 9, 8, 12, 14, 11, 10, 14, 16, 13, 12, 16, 18, 15, 14, 18, 20, 17, 16, 20, 22, 19, 18, 22, 24, 21, 20, 24, 26, 23, 22, 26, 28, 25, 24, 28, ...

MCS6854701 : A₀ = -1; A₁ = -2; A_K+1 = - A_K-1 + K (score: 5)

2, 4, 1, 1, 0, 4, 5, 7, 4, 4, 3, 7, 8, 10, 7, 7, 6, 10, 11, 13, 10, 10, 9, 13, 14, 16, 13, 13, 12, 16, 17, 19, 16, 16, 15, 19, 20, 22, 19, 19, 18, 22, 23, 25, 22, 22, 21, 25, 26, 28, 25, 25, 24, ...

MCS1589640 : A₀ = 1; A₁ = 2; A₂ = 4; A_K+1 = - A_K-2 + K (score: 5)

2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, ...

MCS393480 : A₀ = 1; A₁ = 2; A₂ = 4; A_N = A_N-3 (score: 4)

2, 4, 2, 1, 4, 6, 4, 3, 6, 8, 6, 5, 8, 10, 8, 7, 10, 12, 10, 9, 12, 14, 12, 11, 14, 16, 14, 13, 16, 18, 16, 15, 18, 20, 18, 17, 20, 22, 20, 19, 22, 24, 22, 21, 24, 26, 24, 23, 26, 28, 26, 25, 28, ...

MCS3478277 : A₀ = 0; A₁ = -1; A_K+1 = - A_K-1 + K + 1 (score: 5)

2, 4, 2, 3, 5, 3, 4, 6, 4, 5, 7, 5, 6, 8, 6, 7, 9, 7, 8, 10, 8, 9, 11, 9, 10, 12, 10, 11, 13, 11, 12, 14, 12, 13, 15, 13, 14, 16, 14, 15, 17, 15, 16, 18, 16, 17, 19, 17, 18, 20, 18, 19, 21, 19, ...

MCS1638664 : A₀ = 1; A₁ = 2; A₂ = 4; A_N = A_N-3 + 1 (score: 5)

2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, ...

MCS854034 : A₀ = 2; A₁ = 4; A_N = A_N-2 (score: 4)

Horadam sequence W_n(2, 4; 1, 0)

2, 4, 2, 4, 8, 4, 8, 16, 8, 16, 32, 16, 32, 64, 32, 64, 128, 64, 128, 256, 128, 256, 512, 256, 512, 1024, 512, 1024, 2048, 1024, 2048, 4096, 2048, 4096, 8192, 4096, 8192, 16384, 8192, 16384, ...

MCS787080 : A₀ = 1; A₁ = 2; A₂ = 4; A_N = 2 A_N-3 (score: 5)

2, 4, 2, 8, 6, 32, 30, 192, 210, 1536, 1890, 15360, 20790, 184320, 270270, 2580480, 4054050, 41287680, 68918850, 743178240, 1309458150, 14863564800, 27498621150, 326998425600, 632468286450, ...

MCS852114 : A₀ = 2; A₁ = 4; A_K+1 = K A_K-1 (score: 5)

2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20, 19, 21, 20, 22, 21, 23, 22, 24, 23, 25, 24, 26, 25, 27, 26, 28, 27, 29, ...

MCS3475474 : A₀ = 2; A₁ = 4; A_N = A_N-2 + 1 (score: 5)

2, 4, 3, 5, 8, 8, 11, 15, 16, 20, 25, 27, 32, 38, 41, 47, 54, 58, 65, 73, 78, 86, 95, 101, 110, 120, 127, 137, 148, 156, 167, 179, 188, 200, 213, 223, 236, 250, 261, 275, 290, 302, 317, 333, 346, ...

MCS1589512 : A₀ = 1; A₁ = 2; A₂ = 4; A_K+1 = A_K-2 + K (score: 5)

2, 4, 3, 6, 6, 10, 11, 16, 18, 24, 27, 34, 38, 46, 51, 60, 66, 76, 83, 94, 102, 114, 123, 136, 146, 160, 171, 186, 198, 214, 227, 244, 258, 276, 291, 310, 326, 346, 363, 384, 402, 424, 443, 466, ...

MCS3426322 : A₀ = 2; A₁ = 4; A_K+1 = A_K-1 + K (score: 5)

2, 4, 3, 6, 7, 9, 13, 16, 22, 29, 38, 51, 67, 89, 118, 156, 207, 274, 363, 481, 637, 844, 1118, 1481, 1962, 2599, 3443, 4561, 6042, 8004, 10603, 14046, 18607, 24649, 32653, 43256, 57302, 75909, ...

MCS1581320 : A₀ = 1; A₁ = 2; A₂ = 4; A_N = A_N-2 + A_N-3 (score: 5)

2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

MCS248418 : A₀ = 2; A_K+1 = - K A_K + 2 A_K (score: 5)

2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 4, 2, ...

MCS1747137 : A₀ = 0; A₁ = 0; A_N = A_N-1 - A_N-2 + 2 (score: 5)

2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, ...

MCS6295762 : A₀ = 2; A₁ = 4; A₂ = 4; A_N = A_N-3 (score: 5)

2, 4, 4, 3, 2, 3, 5, 7, 7, 6, 5, 6, 8, 10, 10, 9, 8, 9, 11, 13, 13, 12, 11, 12, 14, 16, 16, 15, 14, 15, 17, 19, 19, 18, 17, 18, 20, 22, 22, 21, 20, 21, 23, 25, 25, 24, 23, 24, 26, 28, 28, 27, 26, ...

MCS1589637 : A₀ = 0; A₁ = -1; A₂ = 0; A_K+1 = - A_K-2 + K (score: 5)

A zig-zag growing sequence

2, 4, 4, 4, 3, 4, 5, 7, 7, 7, 6, 7, 8, 10, 10, 10, 9, 10, 11, 13, 13, 13, 12, 13, 14, 16, 16, 16, 15, 16, 17, 19, 19, 19, 18, 19, 20, 22, 22, 22, 21, 22, 23, 25, 25, 25, 24, 25, 26, 28, 28, 28, ...

MCS25434294 (alias MCS26805814) : A₀ = 1; A₁ = 1; A₂ = 0; A_K+1 = - A_K-2 + K (score: 5)

2, 4, 4, 4, 6, 8, 8, 8, 10, 12, 12, 12, 14, 16, 16, 16, 18, 20, 20, 20, 22, 24, 24, 24, 26, 28, 28, 28, 30, 32, 32, 32, 34, 36, 36, 36, 38, 40, 40, 40, 42, 44, 44, 44, 46, 48, 48, 48, 50, 52, 52, ...

MCS428737 : A₀ = 0; A₁ = 0; A_K+1 = - A_K-1 + 2 K (score: 4)

2, 4, 4, 7, 10, 11, 15, 19, 21, 26, 31, 34, 40, 46, 50, 57, 64, 69, 77, 85, 91, 100, 109, 116, 126, 136, 144, 155, 166, 175, 187, 199, 209, 222, 235, 246, 260, 274, 286, 301, 316, 329, 345, 361, ...

MCS794757 : A₀ = 0; A₁ = 1; A₂ = 0; A_K+1 = A_K-2 + K (score: 5)

2, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, 128, 128, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 16384, 16384, 32768, 32768, 65536, 65536, 131072, 131072, 262144, 262144, ...

MCS1709074 : A₀ = 2; A₁ = 4; A_N = 2 A_N-2 (score: 5)

Horadam sequence W_n(2, 4; 2, 0)

2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, 4, 5, 2, ...

MCS1573906 : A₀ = 2; A₁ = 4; A₂ = 5; A_N = A_N-3 (score: 5)

2, 4, 5, 3, 2, 2, 5, 7, 8, 6, 5, 5, 8, 10, 11, 9, 8, 8, 11, 13, 14, 12, 11, 11, 14, 16, 17, 15, 14, 14, 17, 19, 20, 18, 17, 17, 20, 22, 23, 21, 20, 20, 23, 25, 26, 24, 23, 23, 26, 28, 29, 27, 26, ...

MCS6358581 : A₀ = 0; A₁ = -1; A₂ = -1; A_K+1 = - A_K-2 + K (score: 5)

2, 4, 5, 5, 5, 6, 8, 10, 11, 11, 11, 12, 14, 16, 17, 17, 17, 18, 20, 22, 23, 23, 23, 24, 26, 28, 29, 29, 29, 30, 32, 34, 35, 35, 35, 36, 38, 40, 41, 41, 41, 42, 44, 46, 47, 47, 47, 48, 50, 52, 53, ...

MCS1722753 : A₀ = -1; A₁ = 0; A_K+1 = A_K - A_K-1 + K (score: 5)

2, 4, 5, 5, 6, 8, 9, 9, 10, 12, 13, 13, 14, 16, 17, 17, 18, 20, 21, 21, 22, 24, 25, 25, 26, 28, 29, 29, 30, 32, 33, 33, 34, 36, 37, 37, 38, 40, 41, 41, 42, 44, 45, 45, 46, 48, 49, 49, 50, 52, 53, ...

MCS13717 (alias MCS6957830) : A₀ = 0; A₁ = 1; A_K+1 = - A_K-1 + 2 K - 1 (score: 5)

2, 4, 5, 6, 6, 7, 8, 10, 11, 12, 12, 13, 14, 16, 17, 18, 18, 19, 20, 22, 23, 24, 24, 25, 26, 28, 29, 30, 30, 31, 32, 34, 35, 36, 36, 37, 38, 40, 41, 42, 42, 43, 44, 46, 47, 48, 48, 49, 50, 52, 53, ...

MCS12449 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = - A_K-2 + 2 K (score: 5)

2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, ...

MCS124641 (alias MCS440448) : A₀ = -1; A_K+1 = - A_K + 3 K (score: 5)

2, 4, 5, 7, 10, 12, 15, 19, 22, 26, 31, 35, 40, 46, 51, 57, 64, 70, 77, 85, 92, 100, 109, 117, 126, 136, 145, 155, 166, 176, 187, 199, 210, 222, 235, 247, 260, 274, 287, 301, 316, 330, 345, 361, ...

MCS198689 (alias MCS1675329, MCS6570246) : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = A_K-2 + K (score: 4)

2, 4, 5, 7, 11, 16, 23, 34, 50, 73, 107, 157, 230, 337, 494, 724, 1061, 1555, 2279, 3340, 4895, 7174, 10514, 15409, 22583, 33097, 48506, 71089, 104186, 152692, 223781, 327967, 480659, 704440, ...

MCS1605896 : A₀ = 1; A₁ = 2; A₂ = 4; A_N = A_N-1 + A_N-3 (score: 5)

2, 4, 5, 8, 13, 16, 23, 34, 41, 56, 79, 94, 125, 172, 203, 266, 361, 424, 551, 742, 869, 1124, 1507, 1762, 2273, 3040, 3551, 4574, 6109, 7132, 9179, 12250, 14297, 18392, 24535, 28630, 36821, ...

MCS3179142 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = 2 A_K-2 + K (score: 5)

2, 4, 6, 7, 7, 7, 8, 10, 12, 13, 13, 13, 14, 16, 18, 19, 19, 19, 20, 22, 24, 25, 25, 25, 26, 28, 30, 31, 31, 31, 32, 34, 36, 37, 37, 37, 38, 40, 42, 43, 43, 43, 44, 46, 48, 49, 49, 49, 50, 52, 54, ...

MCS3445510 (alias MCS27465, MCS13931270) : A₀ = 1; A₁ = 1; A_K+1 = A_K - A_K-1 + K (score: 4)

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, ...

MCS882 (alias MCS490, MCS7082, MCS7706, MCS14170, MCS61652, MCS215648, MCS251138, MCS993986)

A_K = 2 K (score: 2)

Even numbers (A005843)

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

2, 4, 6, 8, 11, 14, 17, 21, 25, 29, 34, 39, 44, 50, 56, 62, 69, 76, 83, 91, 99, 107, 116, 125, 134, 144, 154, 164, 175, 186, 197, 209, 221, 233, 246, 259, 272, 286, 300, 314, 329, 344, 359, 375, ...

MCS3179021 : A₀ = -1; A₁ = -1; A₂ = 0; A_K+1 = A_K-2 + K (score: 5)

2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 110, 121, 132, 144, 156, 169, 182, 196, 210, 225, 240, 256, 272, 289, 306, 324, 342, 361, 380, 400, 420, 441, 462, 484, 506, ...

MCS214145 (alias MCS3396, MCS877697, MCS1746048)

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

Squares and Semisquares: floor(N²/4) (A002620)

2, 4, 6, 9, 14, 21, 31, 46, 68, 100, 147, 216, 317, 465, 682, 1000, 1466, 2149, 3150, 4617, 6767, 9918, 14536, 21304, 31223, 45760, 67065, 98289, 144050, 211116, 309406, 453457, 664574, 973981, ...

MCS823329 (alias MCS6586630) : A₀ = 0; A₁ = 1; A₂ = 1; A_N = A_N-1 + A_N-3 + 1 (score: 5)

2, 4, 6, 10, 14, 22, 30, 46, 62, 94, 126, 190, 254, 382, 510, 766, 1022, 1534, 2046, 3070, 4094, 6142, 8190, 12286, 16382, 24574, 32766, 49150, 65534, 98302, 131070, 196606, 262142, 393214, ...

MCS6818 (alias MCS872768) : A₀ = 0; A₁ = 1; A_N = 2 A_N-2 + 2 (score: 5)

2, 4, 6, 10, 15, 22, 32, 45, 63, 87, 119, 162, 219, 295, 396, 530, 708, 944, 1257, 1672, 2222, 2951, 3917, 5197, 6893, 9140, 12117, 16061, 21286, 28208, 37378, 49526, 65619, 86938, 115180, 152593, ...

MCS6365446 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K-1 + A_K-2 + K (score: 5)

2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, ...

MCS3442706 : A₀ = 2; A₁ = 4; A_N = A_N-1 + A_N-2 (score: 5)

Horadam sequence W_n(2, 4; 1, 1)

2, 4, 6, 10, 18, 30, 50, 86, 146, 246, 418, 710, 1202, 2038, 3458, 5862, 9938, 16854, 28578, 48454, 82162, 139318, 236226, 400550, 679186, 1151638, 1952738, 3311110, 5614386, 9519862, 16142082, ...

MCS3211910 : A₀ = 1; A₁ = 1; A₂ = 2; A_N = A_N-1 + 2 A_N-3 (score: 5)

2, 4, 7, 10, 14, 19, 24, 30, 37, 44, 52, 61, 70, 80, 91, 102, 114, 127, 140, 154, 169, 184, 200, 217, 234, 252, 271, 290, 310, 331, 352, 374, 397, 420, 444, 469, 494, 520, 547, 574, 602, 631, 660, ...

MCS6224 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = A_K-2 + 2 K (score: 5)

2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, ...

MCS31008 (alias MCS125216, MCS251272, MCS1004674, MCS1739392, MCS1742016, MCS6968070, MCS7023110)

A₀ = 1; A_K+1 = A_K + K (score: 2)

Slicing a Pancake, or Central Polygonal numbers (A000124)

2, 4, 7, 11, 17, 25, 36, 51, 71, 98, 134, 182, 246, 331, 444, 594, 793, 1057, 1407, 1871, 2486, 3301, 4381, 5812, 7708, 10220, 13548, 17957, 23798, 31536, 41787, 55367, 73357, 97189, 128760, ...

MCS1591361 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = A_K-1 + A_K-2 + K (score: 5)

2, 4, 7, 12, 18, 24, 31, 40, 50, 60, 71, 84, 98, 112, 127, 144, 162, 180, 199, 220, 242, 264, 287, 312, 338, 364, 391, 420, 450, 480, 511, 544, 578, 612, 647, 684, 722, 760, 799, 840, 882, 924, ...

MCS427585 : A₀ = -1; A₁ = 0; A_K+1 = - A_K-1 + K² (score: 5)

2, 4, 7, 12, 19, 30, 45, 68, 99, 146, 209, 304, 431, 622, 877, 1260, 1771, 2538, 3561, 5096, 7143, 10214, 14309, 20452, 28643, 40930, 57313, 81888, 114655, 163806, 229341, 327644, 458715, 655322, ...

MCS1739072 : A₀ = 1; A₁ = 2; A_K+1 = 2 A_K-1 + K + 1 (score: 5)

2, 4, 7, 12, 20, 33, 54, 88, 143, 232, 376, 609, 986, 1596, 2583, 4180, 6764, 10945, 17710, 28656, 46367, 75024, 121392, 196417, 317810, 514228, 832039, 1346268, 2178308, 3524577, 5702886, ...

MCS3400 (alias MCS12609, MCS807009, MCS870528, MCS870529, MCS1741057, MCS3482117)

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

2, 4, 7, 12, 21, 38, 71, 136, 265, 522, 1035, 2060, 4109, 8206, 16399, 32784, 65553, 131090, 262163, 524308, 1048597, 2097174, 4194327, 8388632, 16777241, 33554458, 67108891, 134217756, 268435485, ...

MCS248514 : A₀ = 2; A_K+1 = 2 A_K - K (score: 4)

2, 4, 7, 13, 22, 40, 67, 121, 202, 364, 607, 1093, 1822, 3280, 5467, 9841, 16402, 29524, 49207, 88573, 147622, 265720, 442867, 797161, 1328602, 2391484, 3985807, 7174453, 11957422, 21523360, ...

MCS434624 : A₀ = 1; A₁ = 2; A_N = 3 A_N-2 + 1 (score: 5)

2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317, 410744, 755476, 1389537, 2555757, 4700770, 8646064, 15902591, 29249425, 53798080, ...

MCS803873 (alias MCS1607745, MCS6430982) : A₀ = 0; A₁ = 1; A₂ = 1; A_N = A_N-1 + A_N-2 + A_N-3 (score: 5)

2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, 84, 98, 112, 128, 144, 162, 180, 200, 220, 242, 264, 288, 312, 338, 364, 392, 420, 450, 480, 512, 544, 578, 612, 648, 684, 722, 760, 800, 840, 882, 924, ...

MCS7784 (alias MCS7788, MCS428673) : A₀ = 0; A_K+1 = - A_K + K² + K (score: 4)

2, 4, 8, 13, 18, 24, 32, 41, 50, 60, 72, 85, 98, 112, 128, 145, 162, 180, 200, 221, 242, 264, 288, 313, 338, 364, 392, 421, 450, 480, 512, 545, 578, 612, 648, 685, 722, 760, 800, 841, 882, 924, ...

MCS13580 : A₀ = 0; A₁ = 1; A_K+1 = - A_K-1 + K² + 1 (score: 5)

2, 4, 8, 13, 20, 28, 38, 49, 62, 76, 92, 109, 128, 148, 170, 193, 218, 244, 272, 301, 332, 364, 398, 433, 470, 508, 548, 589, 632, 676, 722, 769, 818, 868, 920, 973, 1028, 1084, 1142, 1201, 1262, ...

MCS429696 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 + 3 K (score: 5)

2, 4, 8, 14, 21, 28, 35, 43, 53, 65, 78, 91, 104, 118, 134, 152, 171, 190, 209, 229, 251, 275, 300, 325, 350, 376, 404, 434, 465, 496, 527, 559, 593, 629, 666, 703, 740, 778, 818, 860, 903, 946, ...

MCS6153 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = - A_K-2 + K² (score: 5)

2, 4, 8, 14, 22, 32, 44, 58, 74, 92, 112, 134, 158, 184, 212, 242, 274, 308, 344, 382, 422, 464, 508, 554, 602, 652, 704, 758, 814, 872, 932, 994, 1058, 1124, 1192, 1262, 1334, 1408, 1484, 1562, ...

MCS14164 : A_K = K² + K + 2 (score: 5)

2, 4, 8, 14, 23, 37, 58, 89, 135, 203, 303, 450, 666, 983, 1448, 2130, 3130, 4596, 6745, 9895, 14512, 21279, 31197, 45733, 67037, 98260, 144020, 211085, 309374, 453424, 664540, 973946, 1427403, ...

MCS12576 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = A_K + A_K-2 + K (score: 5)

2, 4, 8, 14, 24, 38, 60, 90, 136, 198, 292, 418, 608, 862, 1244, 1754, 2520, 3542, 5076, 7122, 10192, 14286, 20428, 28618, 40904, 57286, 81860, 114626, 163776, 229310, 327612, 458682, 655288, ...

MCS857408 : A₀ = 1; A₁ = 2; A_K+1 = 2 A_K-1 + 2 K (score: 5)

2, 4, 8, 14, 24, 40, 66, 108, 176, 286, 464, 752, 1218, 1972, 3192, 5166, 8360, 13528, 21890, 35420, 57312, 92734, 150048, 242784, 392834, 635620, 1028456, 1664078, 2692536, 4356616, 7049154, ...

MCS1747073 : A₀ = 0; A₁ = 0; A_N = A_N-1 + A_N-2 + 2 (score: 5)

2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697, 834, 988, 1160, 1351, 1562, 1794, 2048, 2325, 2626, 2952, 3304, 3683, 4090, 4526, 4992, 5489, 6018, 6580, 7176, 7807, 8474, ...

MCS1725632 : A₀ = 1; A₁ = 2; A_K+1 = 2 A_K - A_K-1 + K (score: 5)

2, 4, 8, 15, 27, 47, 80, 134, 222, 365, 597, 973, 1582, 2568, 4164, 6747, 10927, 17691, 28636, 46346, 75002, 121369, 196393, 317785, 514202, 832012, 1346240, 2178279, 3524547, 5702855, 9227432, ...

MCS861312 (alias MCS14062086) : A₀ = 1; A₁ = 2; A_K+1 = A_K + A_K-1 + K (score: 4)

2, 4, 8, 15, 28, 50, 90, 157, 278, 480, 844, 1451, 2544, 4366, 7646, 13113, 22954, 39356, 68880, 118087, 206660, 354282, 620002, 1062869, 1860030, 3188632, 5580116, 9565923, 16740376, 28697798, ...

MCS428480 : A₀ = 1; A₁ = 2; A_K+1 = 3 A_K-1 + K (score: 5)

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