Munafo's Classical Sequences

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2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, ...

MCS15520 (alias MCS62082, MCS427456, MCS430400)

A₀ = 1; A_N = 2 A_N-1 (score: 2)

Powers of 2 (A000079)

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

2, 4, 8, 17, 38, 88, 208, 497, 1194, 2876, 6936, 16737, 40398, 97520, 235424, 568353, 1372114, 3312564, 7997224, 19306993, 46611190, 112529352, 271669872, 655869073, 1583407994, 3822685036, ...

MCS1726080 : A₀ = 1; A₁ = 2; A_K+1 = 2 A_K + A_K-1 - K (score: 5)

2, 4, 8, 18, 42, 110, 296, 882, 2666, 8822, 29328, 105866, 381266, 1482126, 5718992, 23714018, 97222866, 426852326, 1847234456, 8537046522, 38791923578, 187815023486, 892214242296, ...

MCS27264 : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 + 2 (score: 5)

2, 4, 9, 17, 31, 54, 92, 154, 255, 419, 685, 1116, 1814, 2944, 4773, 7733, 12523, 20274, 32816, 53110, 85947, 139079, 225049, 364152, 589226, 953404, 1542657, 2496089, 4038775, 6534894, 10573700, ...

MCS13781014 : A₀ = 1; A₁ = 0; A_K+1 = A_K + A_K-1 + K (score: 5)

2, 4, 9, 19, 36, 62, 99, 149, 214, 296, 397, 519, 664, 834, 1031, 1257, 1514, 1804, 2129, 2491, 2892, 3334, 3819, 4349, 4926, 5552, 6229, 6959, 7744, 8586, 9487, 10449, 11474, 12564, 13721, 14947, ...

MCS125192 : A₀ = 1; A_K+1 = A_K + K² + 1 (score: 4)

2, 4, 9, 20, 43, 90, 185, 376, 759, 1526, 3061, 6132, 12275, 24562, 49137, 98288, 196591, 393198, 786413, 1572844, 3145707, 6291434, 12582889, 25165800, 50331623, 100663270, 201326565, 402653156, ...

MCS248450 : A₀ = 2; A_K+1 = 2 A_K + K (score: 4)

2, 4, 9, 20, 44, 97, 214, 472, 1041, 2296, 5064, 11169, 24634, 54332, 119833, 264300, 582932, 1285697, 2835694, 6254320, 13794337, 30424368, 67103056, 148000449, 326425266, 719953588, 1587907625, ...

MCS6304 (alias MCS806977) : A₀ = 0; A₁ = 1; A₂ = 2; A_N = 2 A_N-1 + A_N-3 (score: 5)

2, 4, 9, 20, 50, 126, 357, 1016, 3222, 10170, 35453, 122052, 460902, 1708742, 6913545, 27339888, 117530282, 492118002, 2233075377, 9842360060, 46894582938, 216531921342, ...

MCS856102 : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 + K (score: 4)

2, 4, 9, 21, 50, 120, 289, 697, 1682, 4060, 9801, 23661, 57122, 137904, 332929, 803761, 1940450, 4684660, 11309769, 27304197, 65918162, 159140520, 384199201, 927538921, 2239277042, 5406093004, ...

MCS6868 (alias MCS1758336, MCS7033350) : A₀ = 0; A₁ = 1; A_N = 2 A_N-1 + A_N-2 - 1 (score: 5)

2, 4, 9, 22, 53, 122, 269, 574, 1197, 2458, 4997, 10094, 20309, 40762, 81693, 163582, 327389, 655034, 1310357, 2621038, 5242437, 10485274, 20970989, 41942462, 83885453, 167771482, 335543589, ...

MCS248354 : A₀ = 2; A_K+1 = 2 A_K + K² (score: 5)

2, 4, 9, 22, 58, 163, 486, 1525, 5023, 17261, 61801, 229416, 882475, 3503041, 14349016, 60434172, 261785329, 1162598284, 5296140752, 24676349293, 117677694828, 572852174491, ...

MCS196753 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = K A_K-1 + A_K-2 (score: 5)

2, 4, 9, 22, 59, 170, 525, 1716, 5917, 21362, 80533, 315516, 1281913, 5383622, 23330405, 104084736, 477371217, 2246811730, 10839493637, 53528916508, 270318789249, ...

MCS870408 : A₀ = 1; A₁ = 2; A_K+1 = A_K + K A_K-1 + 1 (score: 5)

2, 4, 9, 23, 64, 186, 551, 1645, 4926, 14768, 44293, 132867, 398588, 1195750, 3587235, 10761689, 32285050, 96855132, 290565377, 871696111, 2615088312, 7845264914, 23535794719, 70607384133, ...

MCS252848 : A₀ = 1; A_K+1 = 3 A_K - K - 1 (score: 5)

2, 4, 10, 16, 30, 44, 74, 104, 166, 228, 354, 480, 734, 988, 1498, 2008, 3030, 4052, 6098, 8144, 12238, 16332, 24522, 32712, 49094, 65476, 98242, 131008, 196542, 262076, 393146, 524216, 786358, ...

MCS857409 : A₀ = 0; A₁ = 0; A_K+1 = 2 A_K-1 + 2 K (score: 5)

2, 4, 10, 18, 29, 46, 67, 93, 127, 167, 214, 271, 336, 410, 496, 592, 699, 820, 953, 1099, 1261, 1437, 1628, 1837, 2062, 2304, 2566, 2846, 3145, 3466, 3807, 4169, 4555, 4963, 5394, 5851, 6332, ...

MCS3076 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = A_K-2 + K² (score: 5)

2, 4, 10, 20, 34, 52, 74, 100, 130, 164, 202, 244, 290, 340, 394, 452, 514, 580, 650, 724, 802, 884, 970, 1060, 1154, 1252, 1354, 1460, 1570, 1684, 1802, 1924, 2050, 2180, 2314, 2452, 2594, 2740, ...

MCS14162 : A_K = 2 K² + 2 (score: 5)

2, 4, 10, 23, 49, 97, 182, 328, 574, 983, 1657, 2761, 4562, 7492, 12250, 19967, 32473, 52729, 85526, 138616, 224542, 363599, 588625, 952753, 1541954, 2495332, 4037962, 6534023, 10572769, 17107633, ...

MCS860704 : A₀ = 1; A₁ = 2; A_K+1 = A_K + A_K-1 + K² (score: 5)

2, 4, 10, 24, 54, 116, 242, 496, 1006, 2028, 4074, 8168, 16358, 32740, 65506, 131040, 262110, 524252, 1048538, 2097112, 4194262, 8388564, 16777170, 33554384, 67108814, 134217676, 268435402, ...

MCS496962 : A₀ = 2; A_K+1 = 2 A_K + 2 K (score: 5)

2, 4, 10, 24, 58, 140, 338, 816, 1970, 4756, 11482, 27720, 66922, 161564, 390050, 941664, 2273378, 5488420, 13250218, 31988856, 77227930, 186444716, 450117362, 1086679440, 2623476242, 6333631924, ...

MCS215616 : A₀ = 0; A₁ = 2; A_N = 2 A_N-1 + A_N-2 (score: 5)

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

2, 4, 10, 25, 69, 199, 619, 2019, 6979, 25159, 94959, 371719, 1511239, 6343599, 27500959, 122654959, 562670319, 2647804639, 12775870399, 63084158559, 318601566559, ...

MCS861192 : A₀ = 1; A₁ = 2; A_K+1 = A_K + K A_K-1 + K (score: 5)

2, 4, 10, 26, 64, 148, 326, 694, 1444, 2960, 6010, 12130, 24392, 48940, 98062, 196334, 392908, 786088, 1572482, 3145306, 6290992, 12582404, 25165270, 50331046, 100662644, 201325888, 402652426, ...

MCS248520 : A₀ = 1; A_K+1 = 2 A_K + K² - K (score: 5)

2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568504, 2390480, 10349536, 46206736, 211799312, 997313824, 4809701440, 23758664096, 119952692896, 618884638912, ...

MCS860198 (alias MCS53808, MCS860680, MCS3443750)

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

2, 4, 10, 32, 130, 652, 3914, 27400, 219202, 1972820, 19728202, 217010224, 2604122690, 33853594972, 473950329610, ...

MCS1960 (alias MCS62736, MCS125473, MCS251280)

A₀ = 0; A_K+1 = K A_K + 2 (score: 4)

2, 4, 11, 20, 36, 56, 85, 120, 166, 220, 287, 364, 456, 560, 681, 816, 970, 1140, 1331, 1540, 1772, 2024, 2301, 2600, 2926, 3276, 3655, 4060, 4496, 4960, 5457, 5984, 6546, 7140, 7771, 8436, 9140, ...

MCS3416598 : A₀ = 1; A₁ = 0; A_K+1 = A_K-1 + K² (score: 5)

2, 4, 11, 30, 95, 304, 1063, 3798, 14427, 56204, 229327, 959978, 4170555, 18570224, 85299103, 400992910, 1936376763, 9555242052, 48282777311, 248942860402, ...

MCS3514406 : A₀ = 1; A₁ = 1; A_K+1 = A_K + K A_K-1 - 1 (score: 5)

2, 4, 11, 38, 164, 859, 5319, 38093, 310064, 2828670, 28596765, 317393086, 3837313798, 50202472461, 706671928253, ...

MCS868928 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + A_K-1 + 1 (score: 5)

2, 4, 11, 41, 195, 1130, 7716, 60599, 537676, 5316162, 57940107, 689965123, 8911606493, 124072525780, ...

MCS6790 : A₀ = 0; A₁ = 1; A_K+1 = K A_K - A_K-1 + 1 (score: 5)

2, 4, 11, 42, 206, 1225, 8533, 68058, 611297, 6104437, 67080749, 804357691, 10450545546, 146240556895, ...

MCS6161 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = K A_K - A_K-2 (score: 5)

2, 4, 11, 42, 207, 1238, 8661, 69282, 623531, 6235302, 68588313, 823059746, 10699776687, 149796873606, ...

MCS500944 : A₀ = 1; A_K+1 = K A_K + A_K - K + 1 (score: 5)

2, 4, 12, 24, 70, 156, 504, 1264, 4554, 12660, 50116, 151944, 651534, 2127244, 9773040, 34035936, 166141714, 612646884, 3156692604, 12252937720, 66290544726, 269564629884, ...

MCS428553 : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 + 2 K (score: 5)

2, 4, 12, 32, 120, 384, 1680, 6144, 30240, 122880, 665280, 2949120, 17297280, 82575360, 518918400, 2642411520, 17643225600, 95126814720, 670442572800, ...

MCS426070 : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K-1 (score: 4)

2, 4, 12, 36, 132, 492, 2076, 8964, 42180, 203532, 1047132, 5524836, 30656004, 174301740, 1032669852, 6261722052, 39307157316, 252205707084, ...

MCS430100 : A₀ = 1; A₁ = 2; A_K+1 = A_K + 2 K A_K-1 (score: 5)

2, 4, 12, 43, 188, 988, 6122, 43849, 356922, 3256156, 32918492, 365359579, 4417233452, 57789394468, 813468756018, ...

MCS856640 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + A_K-1 + K (score: 5)

2, 4, 12, 44, 200, 1088, 6928, 50672, 419232, 3874432, 39582784, 443159488, 5397079424, 71048351488, ...

MCS427328 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + 2 A_K-1 (score: 5)

2, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600, 174356582400, ...

MCS248386 : A₀ = 2; A_K+1 = K A_K + 2 A_K (score: 5)

2, 4, 13, 41, 106, 232, 449, 793, 1306, 2036, 3037, 4369, 6098, 8296, 11041, 14417, 18514, 23428, 29261, 36121, 44122, 53384, 64033, 76201, 90026, 105652, 123229, 142913, 164866, 189256, 216257, ...

MCS125188 : A₀ = 1; A_K+1 = A_K + K³ + 1 (score: 5)

2, 4, 13, 54, 274, 1657, 11653, 93498, 843139, 8443043, 92966971, 1116446791, 14522251326, 203404485535, ...

MCS3080 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = K A_K + A_K-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, 1, 2, 5, 1, 2, 5, 1, 2, ...

MCS786964 : A₀ = 1; A₁ = 2; A₂ = 5; A_N = A_N-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, 2, 5, 2, 5, 2, 5, 2, 5, ...

MCS1708074 : A₀ = 2; A₁ = 5; A_N = A_N-2 (score: 5)

Horadam sequence W_n(2, 5; 1, 0)

2, 5, 4, 3, 6, 9, 8, 7, 10, 13, 12, 11, 14, 17, 16, 15, 18, 21, 20, 19, 22, 25, 24, 23, 26, 29, 28, 27, 30, 33, 32, 31, 34, 37, 36, 35, 38, 41, 40, 39, 42, 45, 44, 43, 46, 49, 48, 47, 50, 53, 52, ...

MCS1714949 : A₀ = 0; A₁ = -1; A_K+1 = - A_K-1 + 2 K (score: 5)

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

MCS7023366 : A₀ = 1; A₁ = 1; A_K+1 = - A_K-1 + 2 K - 1 (score: 5)

2, 5, 6, 9, 16, 19, 26, 41, 48, 63, 94, 109, 140, 203, 234, 297, 424, 487, 614, 869, 996, 1251, 1762, 2017, 2528, 3551, 4062, 5085, 7132, 8155, 10202, 14297, 16344, 20439, 28630, 32725, 40916, ...

MCS397393 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = 2 A_K-2 + K (score: 5)

2, 5, 7, 7, 6, 6, 8, 11, 13, 13, 12, 12, 14, 17, 19, 19, 18, 18, 20, 23, 25, 25, 24, 24, 26, 29, 31, 31, 30, 30, 32, 35, 37, 37, 36, 36, 38, 41, 43, 43, 42, 42, 44, 47, 49, 49, 48, 48, 50, 53, 55, ...

MCS3482817 (alias MCS13782038, MCS14062342) : A₀ = 0; A₁ = 0; A_K+1 = A_K - A_K-1 + K + 1 (score: 5)

2, 5, 7, 7, 8, 11, 13, 13, 14, 17, 19, 19, 20, 23, 25, 25, 26, 29, 31, 31, 32, 35, 37, 37, 38, 41, 43, 43, 44, 47, 49, 49, 50, 53, 55, 55, 56, 59, 61, 61, 62, 65, 67, 67, 68, 71, 73, 73, 74, 77, ...

MCS1719046 : A₀ = 1; A₁ = 1; A_K+1 = - A_K-1 + 3 K (score: 5)

2, 5, 7, 10, 15, 19, 24, 31, 37, 44, 53, 61, 70, 81, 91, 102, 115, 127, 140, 155, 169, 184, 201, 217, 234, 253, 271, 290, 311, 331, 352, 375, 397, 420, 445, 469, 494, 521, 547, 574, 603, 631, 660, ...

MCS3186950 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K-2 + 2 K (score: 5)

2, 5, 7, 11, 14, 19, 23, 29, 34, 41, 47, 55, 62, 71, 79, 89, 98, 109, 119, 131, 142, 155, 167, 181, 194, 209, 223, 239, 254, 271, 287, 305, 322, 341, 359, 379, 398, 419, 439, 461, 482, 505, 527, ...

MCS6956045 : A₀ = -1; A₁ = -1; A_K+1 = A_K-1 + K + 1 (score: 5)

2, 5, 7, 11, 18, 25, 31, 39, 50, 61, 71, 83, 98, 113, 127, 143, 162, 181, 199, 219, 242, 265, 287, 311, 338, 365, 391, 419, 450, 481, 511, 543, 578, 613, 647, 683, 722, 761, 799, 839, 882, 925, ...

MCS1710349 : A₀ = -1; A₁ = -1; A_K+1 = - A_K-1 + K² (score: 5)

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, ...

MCS3547 (alias MCS7083, MCS126593, MCS253186)

A_K = 3 K - 1 (score: 4)

2, 5, 8, 12, 18, 25, 32, 40, 50, 61, 72, 84, 98, 113, 128, 144, 162, 181, 200, 220, 242, 265, 288, 312, 338, 365, 392, 420, 450, 481, 512, 544, 578, 613, 648, 684, 722, 761, 800, 840, 882, 925, ...

MCS869153 : A₀ = 0; A₁ = 0; A_K+1 = - A_K-1 + K² + 1 (score: 5)

2, 5, 8, 13, 18, 25, 32, 41, 50, 61, 72, 85, 98, 113, 128, 145, 162, 181, 200, 221, 242, 265, 288, 313, 338, 365, 392, 421, 450, 481, 512, 545, 578, 613, 648, 685, 722, 761, 800, 841, 882, 925, ...

MCS1674 (alias MCS31336, MCS501448) : A₀ = 0; A₁ = 1; A_K+1 = A_K-1 + 2 K (score: 4)

2, 5, 8, 15, 22, 37, 52, 83, 114, 177, 240, 367, 494, 749, 1004, 1515, 2026, 3049, 4072, 6119, 8166, 12261, 16356, 24547, 32738, 49121, 65504, 98271, 131038, 196573, 262108, 393179, 524250, ...

MCS428353 (alias MCS13586, MCS1755457) : A₀ = 0; A₁ = 0; A_K+1 = 2 A_K-1 + K (score: 4)

2, 5, 9, 12, 13, 13, 14, 17, 21, 24, 25, 25, 26, 29, 33, 36, 37, 37, 38, 41, 45, 48, 49, 49, 50, 53, 57, 60, 61, 61, 62, 65, 69, 72, 73, 73, 74, 77, 81, 84, 85, 85, 86, 89, 93, 96, 97, 97, 98, ...

MCS6892294 : A₀ = 1; A₁ = 1; A_K+1 = A_K - A_K-1 + 2 K (score: 5)

2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170, 189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527, 560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, ...

MCS3924 (alias MCS250433) : A₀ = 0; A_K+1 = A_K + K + 2 (score: 4)

2, 5, 9, 15, 25, 40, 62, 95, 144, 216, 322, 478, 707, 1043, 1536, 2259, 3319, 4873, 7151, 10490, 15384, 22557, 33070, 48478, 71060, 104156, 152661, 223749, 327934, 480625, 704405, 1032371, ...

MCS6439174 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K + A_K-2 + K (score: 5)

2, 5, 9, 16, 27, 43, 67, 103, 156, 234, 349, 518, 766, 1130, 1664, 2447, 3595, 5278, 7745, 11361, 16661, 24429, 35814, 52500, 76955, 112796, 165324, 242308, 355134, 520489, 762829, 1117996, ...

MCS6439181 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = A_K + A_K-2 + K (score: 5)

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; A_N = A_N-1 + A_N-2 + 2 (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; A_K+1 = - A_K-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) : A_K = K² + 1 (score: 3)

Squares plus one (A002522)

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; A_K+1 = A_K-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; A_K+1 = A_K + A_K-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; A_K+1 = 2 A_K - 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; A_N = A_N-1 + 2 A_N-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 (alias MCS856841) : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 + K + 1 (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; A_K+1 = A_K-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; A_K+1 = A_K + A_K-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; A_K+1 = A_K + 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; A_K+1 = A_K + A_K-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; A_N = 2 A_N-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; A_K+1 = A_K + 2 A_K-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; A_N = 2 A_N-1 + A_N-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; A_N = A_N-1 + 3 A_N-2 (score: 5)

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

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

2^N-N (A000325)

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

Pell Numbers (A000129)

Horadam sequence W_n(0, 1; 1, 2) ; Horadam sequence W_n(1, 2; 1, 2) ; Horadam sequence W_n(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; A_K+1 = A_K + K A_K-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; A_N = 3 A_N-1 - A_N-2 (score: 5)

Odd-numbered Fibonacci numbers (A001519)

Horadam sequence W_n(1, 1; -1, 3) ; Horadam sequence W_n(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; A_K+1 = A_K + 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; A_K+1 = 2 A_K + 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; A_N = 3 A_N-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; A_K+1 = 2 A_K + K A_K-1 (score: 5)

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

MCS7844 (alias MCS15540, MCS15668, MCS251024, MCS501392)

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

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

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

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

MCS976 (alias MCS3916, MCS15660, MCS31248, MCS62497, MCS125200, MCS125328)

A₀ = 0; A_K+1 = K A_K + 1 (score: 3)

Distinct Ordered Subsets of Set with N Elements (A000522)

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

MCS854278 (alias MCS860736, MCS3459334) : A₀ = 1; A₁ = 1; A_K+1 = K A_K + A_K-1 (score: 4)

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, ...

MCS6726 (alias MCS427649) : A₀ = 0; A₁ = 1; A_K+1 = K A_K + A_K - A_K-1 (score: 5)

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