Munafo's Classical Sequences

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2, 3, 3, 4, 6, 7, 9, 12, 14, 17, 21, 24, 28, 33, 37, 42, 48, 53, 59, 66, 72, 79, 87, 94, 102, 111, 119, 128, 138, 147, 157, 168, 178, 189, 201, 212, 224, 237, 249, 262, 276, 289, 303, 318, 332, ...

MCS6358066 : A₀ = 2; A₁ = 3; A₂ = 3; A_K+1 = A_K-2 + K (score: 5)

2, 3, 3, 4, 6, 8, 11, 16, 23, 33, 48, 70, 102, 149, 218, 319, 467, 684, 1002, 1468, 2151, 3152, 4619, 6769, 9920, 14538, 21306, 31225, 45762, 67067, 98291, 144052, 211118, 309408, 453459, 664576, ...

MCS1679424 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = A_N-1 + A_N-3 - 1 (score: 5)

2, 3, 3, 5, 5, 9, 9, 17, 17, 33, 33, 65, 65, 129, 129, 257, 257, 513, 513, 1025, 1025, 2049, 2049, 4097, 4097, 8193, 8193, 16385, 16385, 32769, 32769, 65537, 65537, 131073, 131073, 262145, 262145, ...

MCS1754370 : A₀ = 2; A₁ = 3; A_N = 2 A_N-2 - 1 (score: 5)

2, 3, 3, 5, 6, 8, 11, 14, 19, 25, 33, 44, 58, 77, 102, 135, 179, 237, 314, 416, 551, 730, 967, 1281, 1697, 2248, 2978, 3945, 5226, 6923, 9171, 12149, 16094, 21320, 28243, 37414, 49563, 65657, ...

MCS395328 (alias MCS6325298) : A₀ = 1; A₁ = 2; A₂ = 3; A_N = A_N-2 + A_N-3 (score: 4)

2, 3, 3, 5, 6, 9, 11, 15, 18, 23, 27, 33, 38, 45, 51, 59, 66, 75, 83, 93, 102, 113, 123, 135, 146, 159, 171, 185, 198, 213, 227, 243, 258, 275, 291, 309, 326, 345, 363, 383, 402, 423, 443, 465, ...

MCS856578 : A₀ = 2; A₁ = 3; A_K+1 = A_K-1 + K (score: 4)

2, 3, 3, 5, 7, 7, 11, 15, 15, 23, 31, 31, 47, 63, 63, 95, 127, 127, 191, 255, 255, 383, 511, 511, 767, 1023, 1023, 1535, 2047, 2047, 3071, 4095, 4095, 6143, 8191, 8191, 12287, 16383, 16383, 24575, ...

MCS819360 (alias MCS3277446) : A₀ = 1; A₁ = 2; A₂ = 3; A_N = 2 A_N-3 + 1 (score: 5)

2, 3, 3, 5, 7, 8, 11, 14, 16, 20, 24, 27, 32, 37, 41, 47, 53, 58, 65, 72, 78, 86, 94, 101, 110, 119, 127, 137, 147, 156, 167, 178, 188, 200, 212, 223, 236, 249, 261, 275, 289, 302, 317, 332, 346, ...

MCS397376 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = A_K-2 + K (score: 4)

2, 3, 3, 5, 8, 11, 16, 24, 35, 51, 75, 110, 161, 236, 346, 507, 743, 1089, 1596, 2339, 3428, 5024, 7363, 10791, 15815, 23178, 33969, 49784, 72962, 106931, 156715, 229677, 336608, 493323, 723000, ...

MCS200736 (alias MCS6423602) : A₀ = 0; A₁ = 2; A₂ = 3; A_N = A_N-1 + A_N-3 (score: 5)

2, 3, 3, 6, 9, 9, 18, 27, 27, 54, 81, 81, 162, 243, 243, 486, 729, 729, 1458, 2187, 2187, 4374, 6561, 6561, 13122, 19683, 19683, 39366, 59049, 59049, 118098, 177147, 177147, 354294, 531441, ...

MCS196832 (alias MCS787334) : A₀ = 1; A₁ = 2; A₂ = 3; A_N = 3 A_N-3 (score: 5)

2, 3, 3, 7, 9, 10, 15, 18, 20, 26, 30, 33, 40, 45, 49, 57, 63, 68, 77, 84, 90, 100, 108, 115, 126, 135, 143, 155, 165, 174, 187, 198, 208, 222, 234, 245, 260, 273, 285, 301, 315, 328, 345, 360, ...

MCS6358061 : A₀ = 0; A₁ = 0; A₂ = -1; A_K+1 = A_K-2 + K (score: 5)

2, 3, 3, 7, 9, 32, 47, 215, 344, 1888, 3225, 20424, 36812, 262287, 494944, 3897493, 7656817, 65762437, 133925213, 1241829486, 2612741823, 25944493993, 56238490620, 594110620016, ...

MCS393632 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = K A_K-1 - A_K-2 (score: 5)

2, 3, 3, 7, 10, 29, 51, 175, 358, 1401, 3223, 14011, 35454, 168133, 460903, 2353863, 6913546, 37661809, 117530283, 677912563, 2233075378, 13558251261, 46894582939, 298281527743, ...

MCS868386 : A₀ = 2; A₁ = 3; A_K+1 = K A_K-1 + 1 (score: 5)

2, 3, 3, 7, 12, 23, 37, 59, 86, 123, 167, 223, 288, 367, 457, 563, 682, 819, 971, 1143, 1332, 1543, 1773, 2027, 2302, 2603, 2927, 3279, 3656, 4063, 4497, 4963, 5458, 5987, 6547, 7143, 7772, 8439, ...

MCS854146 : A₀ = 2; A₁ = 3; A_K+1 = A_K-1 + K² (score: 5)

2, 3, 3, 7, 13, 22, 29, 36, 42, 52, 64, 79, 92, 105, 117, 133, 151, 172, 191, 210, 228, 250, 274, 301, 326, 351, 375, 403, 433, 466, 497, 528, 558, 592, 628, 667, 704, 741, 777, 817, 859, 904, ...

MCS393824 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = - A_K-2 + K² (score: 5)

2, 3, 3, 8, 12, 36, 65, 222, 462, 1784, 4167, 17850, 45848, 214212, 596037, 2998982, 8940570, 47983728, 151989707, 863707122, 2887804452, 17274142460, 60643893513, 380031134142, ...

MCS856098 : A₀ = 2; A₁ = 3; A_K+1 = K A_K-1 + K (score: 5)

2, 3, 4, 0, 0, 0, 5, 6, 7, 3, 3, 3, 8, 9, 10, 6, 6, 6, 11, 12, 13, 9, 9, 9, 14, 15, 16, 12, 12, 12, 17, 18, 19, 15, 15, 15, 20, 21, 22, 18, 18, 18, 23, 24, 25, 21, 21, 21, 26, 27, 28, 24, 24, 24, ...

MCS1589634 : A₀ = 2; A₁ = 3; A₂ = 4; A_K+1 = - A_K-2 + K (score: 5)

2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, ...

MCS393474 : A₀ = 2; A₁ = 3; A₂ = 4; A_N = A_N-3 (score: 4)

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

MCS1589645 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = - A_K-2 + K (score: 4)

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

MCS1638658 : A₀ = 2; A₁ = 3; A₂ = 4; A_N = A_N-3 + 1 (score: 5)

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

MCS6358582 (alias MCS837681, MCS26281526) : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = - A_K-2 + K (score: 4)

2, 3, 4, 4, 6, 8, 8, 12, 16, 16, 24, 32, 32, 48, 64, 64, 96, 128, 128, 192, 256, 256, 384, 512, 512, 768, 1024, 1024, 1536, 2048, 2048, 3072, 4096, 4096, 6144, 8192, 8192, 12288, 16384, 16384, ...

MCS787074 : A₀ = 2; A₁ = 3; A₂ = 4; A_N = 2 A_N-3 (score: 5)

2, 3, 4, 4, 6, 8, 9, 12, 15, 17, 21, 25, 28, 33, 38, 42, 48, 54, 59, 66, 73, 79, 87, 95, 102, 111, 120, 128, 138, 148, 157, 168, 179, 189, 201, 213, 224, 237, 250, 262, 276, 290, 303, 318, 333, ...

MCS1589506 : A₀ = 2; A₁ = 3; A₂ = 4; A_K+1 = A_K-2 + K (score: 5)

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, ...

MCS220 (alias MCS244, MCS884, MCS886, MCS1704, MCS1770, MCS1926, MCS3349, MCS3369, MCS6729, MCS7829, MCS7834, MCS24865, MCS25121, MCS30824, MCS31296, MCS61649, MCS62128, MCS62593, MCS125186, MCS431296, MCS436352, MCS505505, MCS862593, MCS872705, MCS1010370, MCS1607776, MCS1609824, MCS1725186, MCS1745410, MCS3447298, MCS3482816, MCS3483264)

A_K = K (score: 1)

Natural numbers or positive integers (A000027)

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

2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, ...

MCS1581314 : A₀ = 2; A₁ = 3; A₂ = 4; A_N = A_N-2 + A_N-3 (score: 5)

2, 3, 4, 6, 8, 10, 13, 16, 19, 23, 27, 31, 36, 41, 46, 52, 58, 64, 71, 78, 85, 93, 101, 109, 118, 127, 136, 146, 156, 166, 177, 188, 199, 211, 223, 235, 248, 261, 274, 288, 302, 316, 331, 346, ...

MCS1589510 (alias MCS1642560, MCS26805302) : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K-2 + K (score: 4)

2, 3, 4, 6, 8, 11, 14, 18, 22, 27, 32, 38, 44, 51, 58, 66, 74, 83, 92, 102, 112, 123, 134, 146, 158, 171, 184, 198, 212, 227, 242, 258, 274, 291, 308, 326, 344, 363, 382, 402, 422, 443, 464, 486, ...

MCS3478018 : A₀ = 2; A₁ = 3; A_K+1 = A_K-1 + K + 1 (score: 5)

2, 3, 4, 6, 8, 11, 15, 20, 27, 36, 48, 64, 85, 113, 150, 199, 264, 350, 464, 615, 815, 1080, 1431, 1896, 2512, 3328, 4409, 5841, 7738, 10251, 13580, 17990, 23832, 31571, 41823, 55404, 73395, ...

MCS820257 (alias MCS1640512, MCS1640513, MCS6562054, MCS6562061)

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

2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, ...

MCS427266 : A₀ = 2; A₁ = 3; A_N = 2 A_N-2 (score: 4)

Horadam sequence W_n(2, 3; 2, 0)

2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, ...

MCS200737 (alias MCS401472, MCS401473, MCS802945, MCS802949, MCS1605890, MCS1605894, MCS6423606, MCS25694422)

A₀ = 0; A₁ = 1; A₂ = 1; A_N = A_N-1 + A_N-3 (score: 4)

2, 3, 4, 6, 9, 14, 22, 35, 56, 90, 145, 234, 378, 611, 988, 1598, 2585, 4182, 6766, 10947, 17712, 28658, 46369, 75026, 121394, 196419, 317812, 514230, 832041, 1346270, 2178310, 3524579, 5702888, ...

MCS3514882 : A₀ = 2; A₁ = 3; A_N = A_N-1 + A_N-2 - 1 (score: 5)

2, 3, 4, 7, 9, 11, 15, 18, 21, 26, 30, 34, 40, 45, 50, 57, 63, 69, 77, 84, 91, 100, 108, 116, 126, 135, 144, 155, 165, 175, 187, 198, 209, 222, 234, 246, 260, 273, 286, 301, 315, 329, 345, 360, ...

MCS1589517 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = A_K-2 + K (score: 4)

2, 3, 4, 7, 10, 13, 20, 27, 34, 49, 64, 79, 110, 141, 172, 235, 298, 361, 488, 615, 742, 997, 1252, 1507, 2018, 2529, 3040, 4063, 5086, 6109, 8156, 10203, 12250, 16345, 20440, 24535, 32726, 40917, ...

MCS794784 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = 2 A_K-2 + K (score: 5)

2, 3, 4, 7, 10, 15, 20, 27, 34, 43, 52, 63, 74, 87, 100, 115, 130, 147, 164, 183, 202, 223, 244, 267, 290, 315, 340, 367, 394, 423, 452, 483, 514, 547, 580, 615, 650, 687, 724, 763, 802, 843, 884, ...

MCS1714690 : A₀ = 2; A₁ = 3; A_K+1 = A_K-1 + 2 K (score: 5)

2, 3, 4, 7, 10, 15, 24, 35, 54, 83, 124, 191, 290, 439, 672, 1019, 1550, 2363, 3588, 5463, 8314, 12639, 19240, 29267, 44518, 67747, 103052, 156783, 238546, 362887, 552112, 839979, 1277886, ...

MCS790688 (alias MCS3162758) : A₀ = 1; A₁ = 2; A₂ = 3; A_N = A_N-2 + 2 A_N-3 (score: 5)

2, 3, 4, 9, 12, 15, 26, 33, 40, 63, 78, 93, 140, 171, 202, 297, 360, 423, 614, 741, 868, 1251, 1506, 1761, 2528, 3039, 3550, 5085, 6108, 7131, 10202, 12249, 14296, 20439, 24534, 28629, 40916, ...

MCS3179149 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = 2 A_K-2 + K (score: 5)

2, 3, 4, 9, 16, 45, 96, 315, 768, 2835, 7680, 31185, 92160, 405405, 1290240, 6081075, 20643840, 103378275, 371589120, 1964187225, 7431782400, 41247931725, 163499212800, 948702429675, ...

MCS854050 : A₀ = 2; A₁ = 3; A_K+1 = K A_K-1 + A_K-1 (score: 5)

2, 3, 4, 12, 24, 96, 240, 1152, 3360, 18432, 60480, 368640, 1330560, 8847360, 34594560, 247726080, 1037836800, 7927234560, 35286451200, 285380444160, ...

MCS426066 : A₀ = 2; A₁ = 3; A_K+1 = 2 K A_K-1 (score: 5)

2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, ...

MCS1573922 : A₀ = 2; A₁ = 3; A₂ = 5; A_N = A_N-3 (score: 5)

2, 3, 5, 3, 3, 2, 5, 6, 8, 6, 6, 5, 8, 9, 11, 9, 9, 8, 11, 12, 14, 12, 12, 11, 14, 15, 17, 15, 15, 14, 17, 18, 20, 18, 18, 17, 20, 21, 23, 21, 21, 20, 23, 24, 26, 24, 24, 23, 26, 27, 29, 27, 27, ...

MCS6358573 : A₀ = 0; A₁ = 0; A₂ = -1; A_K+1 = - A_K-2 + K (score: 5)

2, 3, 5, 6, 7, 7, 8, 9, 11, 12, 13, 13, 14, 15, 17, 18, 19, 19, 20, 21, 23, 24, 25, 25, 26, 27, 29, 30, 31, 31, 32, 33, 35, 36, 37, 37, 38, 39, 41, 42, 43, 43, 44, 45, 47, 48, 49, 49, 50, 51, 53, ...

MCS3187078 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - A_K-2 + 2 K (score: 5)

2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 35, 40, 45, 51, 57, 63, 70, 77, 84, 92, 100, 108, 117, 126, 135, 145, 155, 165, 176, 187, 198, 210, 222, 234, 247, 260, 273, 287, 301, 315, 330, 345, 360, ...

MCS397377 (alias MCS12832, MCS6701325) : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = A_K-2 + K (score: 4)

floor(N(N-1)/6) (A001840)

2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50, 57, 65, 73, 82, 91, 101, 111, 122, 133, 145, 157, 170, 183, 197, 211, 226, 241, 257, 273, 290, 307, 325, 343, 362, 381, 401, 421, 442, 463, 485, ...

MCS856582 (alias MCS869504, MCS3510790) : A₀ = 1; A₁ = 1; A_K+1 = A_K-1 + K (score: 3)

1 + floor(N²/4) (A033638)

2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 255, 383, 511, 767, 1023, 1535, 2047, 3071, 4095, 6143, 8191, 12287, 16383, 24575, 32767, 49151, 65535, 98303, 131071, 196607, 262143, 393215, ...

MCS434496 (alias MCS1737986) : A₀ = 1; A₁ = 2; A_N = 2 A_N-2 + 1 (score: 4)

2, 3, 5, 8, 11, 13, 14, 15, 17, 20, 23, 25, 26, 27, 29, 32, 35, 37, 38, 39, 41, 44, 47, 49, 50, 51, 53, 56, 59, 61, 62, 63, 65, 68, 71, 73, 74, 75, 77, 80, 83, 85, 86, 87, 89, 92, 95, 97, 98, 99, ...

MCS1723072 : A₀ = 1; A₁ = 2; A_K+1 = A_K - A_K-1 + 2 K (score: 5)

2, 3, 5, 8, 11, 15, 20, 25, 31, 38, 45, 53, 62, 71, 81, 92, 103, 115, 128, 141, 155, 170, 185, 201, 218, 235, 253, 272, 291, 311, 332, 353, 375, 398, 421, 445, 470, 495, 521, 548, 575, 603, 632, ...

MCS796736 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = A_K-2 + 2 K (score: 5)

2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, ...

MCS500866 : A₀ = 2; A_K+1 = A_K + K + 1 (score: 4)

2, 3, 5, 8, 12, 18, 26, 37, 52, 72, 99, 135, 183, 247, 332, 445, 595, 794, 1058, 1408, 1872, 2487, 3302, 4382, 5813, 7709, 10221, 13549, 17958, 23799, 31537, 41788, 55368, 73358, 97190, 128761, ...

MCS1591360 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = A_K-1 + A_K-2 + K (score: 5)

2, 3, 5, 8, 12, 18, 27, 40, 59, 87, 128, 188, 276, 405, 594, 871, 1277, 1872, 2744, 4022, 5895, 8640, 12663, 18559, 27200, 39864, 58424, 85625, 125490, 183915, 269541, 395032, 578948, 848490, ...

MCS12864 (alias MCS1646656, MCS1646657, MCS6586637)

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

2, 3, 5, 8, 13, 20, 31, 46, 69, 100, 147, 210, 305, 432, 623, 878, 1261, 1772, 2539, 3562, 5097, 7144, 10215, 14310, 20453, 28644, 40931, 57314, 81889, 114656, 163807, 229342, 327645, 458716, ...

MCS1713410 : A₀ = 2; A₁ = 3; A_K+1 = 2 A_K-1 + K (score: 5)

2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, ...

MCS840 (alias MCS215168, MCS395809, MCS403505, MCS791616, MCS807008, MCS860674, MCS860678, MCS1721353, MCS3166470, MCS3228038, MCS3442710)

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

Fibonacci numbers (A000045)

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

2, 3, 5, 8, 14, 25, 47, 90, 176, 347, 689, 1372, 2738, 5469, 10931, 21854, 43700, 87391, 174773, 349536, 699062, 1398113, 2796215, 5592418, 11184824, 22369635, 44739257, 89478500, 178956986, ...

MCS1723712 : A₀ = 1; A₁ = 2; A_K+1 = A_K + 2 A_K-1 - K (score: 5)

2, 3, 5, 9, 15, 25, 43, 73, 123, 209, 355, 601, 1019, 1729, 2931, 4969, 8427, 14289, 24227, 41081, 69659, 118113, 200275, 339593, 575819, 976369, 1655555, 2807193, 4759931, 8071041, 13685427, ...

MCS802976 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = A_N-1 + 2 A_N-3 (score: 5)

2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, ...

MCS252546 : A₀ = 2; A_N = 2 A_N-1 - 1 (score: 4)

2, 3, 5, 9, 18, 39, 89, 209, 498, 1195, 2877, 6937, 16738, 40399, 97521, 235425, 568354, 1372115, 3312565, 7997225, 19306994, 46611191, 112529353, 271669873, 655869074, 1583407995, 3822685037, ...

MCS6904326 : A₀ = 1; A₁ = 1; A_K+1 = 2 A_K + A_K-1 - K (score: 5)

2, 3, 5, 10, 20, 37, 63, 100, 150, 215, 297, 398, 520, 665, 835, 1032, 1258, 1515, 1805, 2130, 2492, 2893, 3335, 3820, 4350, 4927, 5553, 6230, 6960, 7745, 8587, 9488, 10450, 11475, 12565, 13722, ...

MCS500770 : A₀ = 2; A_K+1 = A_K + K² + 1 (score: 5)

2, 3, 5, 11, 19, 30, 47, 68, 94, 128, 168, 215, 272, 337, 411, 497, 593, 700, 821, 954, 1100, 1262, 1438, 1629, 1838, 2063, 2305, 2567, 2847, 3146, 3467, 3808, 4170, 4556, 4964, 5395, 5852, 6333, ...

MCS393792 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = A_K-2 + K² (score: 5)

2, 3, 5, 11, 23, 60, 149, 443, 1252, 4136, 12963, 46748, 159692, 620687, 2282436, 9469997, 37139663, 163272385, 677983931, 3139314978, 13722951005, 66603598469, 305044237088, ...

MCS393504 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = K A_K-1 + A_K-2 (score: 5)

2, 3, 5, 11, 26, 70, 200, 620, 2020, 6980, 25160, 94960, 371720, 1511240, 6343600, 27500960, 122654960, 562670320, 2647804640, 12775870400, 63084158560, 318601566560, ...

MCS860194 : A₀ = 2; A₁ = 3; A_K+1 = A_K + K A_K-1 (score: 5)

2, 3, 5, 13, 44, 189, 989, 6123, 43850, 356923, 3256157, 32918493, 365359580, 4417233453, 57789394469, 813468756019, ...

MCS854274 : A₀ = 2; A₁ = 3; A_K+1 = K A_K + A_K-1 (score: 5)

2, 3, 5, 13, 49, 240, 1427, 9940, 79280, 712093, 7110990, 78141610, 936987227, 12173722961, 170353979844, ...

MCS394336 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = K A_K - A_K-2 (score: 5)

2, 3, 6, 8, 10, 14, 17, 20, 25, 29, 33, 39, 44, 49, 56, 62, 68, 76, 83, 90, 99, 107, 115, 125, 134, 143, 154, 164, 174, 186, 197, 208, 221, 233, 245, 259, 272, 285, 300, 314, 328, 344, 359, 374, ...

MCS12716141 : A₀ = -1; A₁ = -1; A₂ = -1; A_K+1 = A_K-2 + K (score: 5)

2, 3, 6, 8, 12, 15, 20, 24, 30, 35, 42, 48, 56, 63, 72, 80, 90, 99, 110, 120, 132, 143, 156, 168, 182, 195, 210, 224, 240, 255, 272, 288, 306, 323, 342, 360, 380, 399, 420, 440, 462, 483, 506, ...

MCS428289 (alias MCS869505, MCS3510789) : A₀ = -1; A₁ = 0; A_K+1 = A_K-1 + K (score: 4)

2, 3, 6, 9, 12, 19, 26, 33, 48, 63, 78, 109, 140, 171, 234, 297, 360, 487, 614, 741, 996, 1251, 1506, 2017, 2528, 3039, 4062, 5085, 6108, 8155, 10202, 12249, 16344, 20439, 24534, 32725, 40916, ...

MCS794785 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = 2 A_K-2 + K (score: 5)

2, 3, 6, 9, 14, 19, 26, 33, 42, 51, 62, 73, 86, 99, 114, 129, 146, 163, 182, 201, 222, 243, 266, 289, 314, 339, 366, 393, 422, 451, 482, 513, 546, 579, 614, 649, 686, 723, 762, 801, 842, 883, 926, ...

MCS428672 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 + 2 K (score: 4)

2, 3, 6, 9, 14, 21, 30, 43, 60, 83, 114, 155, 210, 283, 380, 509, 680, 907, 1208, 1607, 2136, 2837, 3766, 4997, 6628, 8789, 11652, 15445, 20470, 27127, 35946, 47629, 63106, 83609, 110770, 146751, ...

MCS12432 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = A_K-1 + A_K-2 + K (score: 5)

2, 3, 6, 9, 16, 23, 38, 53, 84, 115, 178, 241, 368, 495, 750, 1005, 1516, 2027, 3050, 4073, 6120, 8167, 12262, 16357, 24548, 32739, 49122, 65505, 98272, 131039, 196574, 262109, 393180, 524251, ...

MCS428352 (alias MCS7021830) : A₀ = 1; A₁ = 2; A_K+1 = 2 A_K-1 + K (score: 4)

2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458, 2187, 4374, 6561, 13122, 19683, 39366, 59049, 118098, 177147, 354294, 531441, 1062882, 1594323, 3188646, 4782969, 9565938, 14348907, 28697814, ...

MCS106944 (alias MCS427778) : A₀ = 1; A₁ = 2; A_N = 3 A_N-2 (score: 4)

Horadam sequence W_n(1, 2; 3, 0) ; Horadam sequence W_n(2, 3; 3, 0)

2, 3, 6, 10, 15, 23, 33, 47, 66, 91, 125, 170, 230, 310, 416, 557, 744, 992, 1321, 1757, 2335, 3101, 4116, 5461, 7243, 9604, 12732, 16876, 22366, 29639, 39274, 52038, 68947, 91347, 121021, 160331, ...

MCS6365453 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = A_K-1 + A_K-2 + K (score: 5)

2, 3, 6, 10, 17, 28, 46, 75, 122, 198, 321, 520, 842, 1363, 2206, 3570, 5777, 9348, 15126, 24475, 39602, 64078, 103681, 167760, 271442, 439203, 710646, 1149850, 1860497, 3010348, 4870846, 7881195, ...

MCS435264 (alias MCS3482114, MCS13928470) : A₀ = 0; A₁ = 2; A_N = A_N-1 + A_N-2 + 1 (score: 5)

2, 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, ...

MCS3540 (alias MCS1001794) : A_K = K² + 2 (score: 4)

2, 3, 6, 11, 18, 29, 46, 71, 108, 163, 244, 363, 538, 795, 1172, 1725, 2536, 3725, 5468, 8023, 11768, 17257, 25302, 37093, 54374, 79701, 116820, 171221, 250950, 367799, 539050, 790031, 1157862, ...

MCS1609792 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = A_K + A_K-2 + K (score: 5)

2, 3, 6, 11, 20, 35, 60, 101, 168, 277, 454, 741, 1206, 1959, 3178, 5151, 8344, 13511, 21872, 35401, 57292, 92713, 150026, 242761, 392810, 635595, 1028430, 1664051, 2692508, 4356587, 7049124, ...

MCS3445250 (alias MCS3515520) : A₀ = 2; A₁ = 3; A_K+1 = A_K + A_K-1 + K (score: 5)

2, 3, 6, 11, 20, 37, 68, 125, 230, 423, 778, 1431, 2632, 4841, 8904, 16377, 30122, 55403, 101902, 187427, 344732, 634061, 1166220, 2145013, 3945294, 7256527, 13346834, 24548655, 45152016, ...

MCS12560 (alias MCS1607744) : A₀ = 0; A₁ = 1; A₂ = 2; A_N = A_N-1 + A_N-2 + A_N-3 (score: 5)

2, 3, 6, 11, 22, 43, 86, 171, 342, 683, 1366, 2731, 5462, 10923, 21846, 43691, 87382, 174763, 349526, 699051, 1398102, 2796203, 5592406, 11184811, 22369622, 44739243, 89478486, 178956971, ...

MCS1757504 (alias MCS7030022) : A₀ = 1; A₁ = 2; A_N = A_N-1 + 2 A_N-2 - 1 (score: 5)

2, 3, 6, 11, 26, 57, 158, 401, 1266, 3611, 12662, 39723, 151946, 516401, 2127246, 7746017, 34035938, 131682291, 612646886, 2501963531, 12252937722, 52541234153, 269564629886, ...

MCS436232 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 + 2 (score: 5)

2, 3, 6, 13, 26, 47, 78, 121, 178, 251, 342, 453, 586, 743, 926, 1137, 1378, 1651, 1958, 2301, 2682, 3103, 3566, 4073, 4626, 5227, 5878, 6581, 7338, 8151, 9022, 9953, 10946, 12003, 13126, 14317, ...

MCS500936 : A₀ = 1; A_K+1 = A_K + K² - K + 1 (score: 5)

2, 3, 6, 13, 28, 59, 122, 249, 504, 1015, 2038, 4085, 8180, 16371, 32754, 65521, 131056, 262127, 524270, 1048557, 2097132, 4194283, 8388586, 16777193, 33554408, 67108839, 134217702, 268435429, ...

MCS1010306 : A₀ = 2; A_K+1 = 2 A_K + K - 1 (score: 5)

2, 3, 6, 17, 66, 327, 1958, 13701, 109602, 986411, 9864102, 108505113, 1302061346, 16926797487, 236975164806, ...

MCS7846 (alias MCS251088) : A₀ = 0; A_K+1 = K A_K - K + 2 (score: 5)

2, 3, 7, 10, 16, 21, 29, 36, 46, 55, 67, 78, 92, 105, 121, 136, 154, 171, 191, 210, 232, 253, 277, 300, 326, 351, 379, 406, 436, 465, 497, 528, 562, 595, 631, 666, 704, 741, 781, 820, 862, 903, ...

MCS125320 : A₀ = 1; A_K+1 = - A_K + K² + 1 (score: 4)

2, 3, 7, 13, 24, 39, 61, 89, 126, 171, 227, 293, 372, 463, 569, 689, 826, 979, 1151, 1341, 1552, 1783, 2037, 2313, 2614, 2939, 3291, 3669, 4076, 4511, 4977, 5473, 6002, 6563, 7159, 7789, 8456, ...

MCS868896 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 + K² + 1 (score: 5)

2, 3, 7, 13, 24, 42, 72, 121, 201, 331, 542, 884, 1438, 2335, 3787, 6137, 9940, 16094, 26052, 42165, 68237, 110423, 178682, 289128, 467834, 756987, 1224847, 1981861, 3206736, 5188626, 8395392, ...

MCS430656 : A₀ = 0; A₁ = 2; A_K+1 = A_K + A_K-1 + K (score: 5)

2, 3, 7, 13, 27, 53, 107, 213, 427, 853, 1707, 3413, 6827, 13653, 27307, 54613, 109227, 218453, 436907, 873813, 1747627, 3495253, 6990507, 13981013, 27962027, 55924053, 111848107, 223696213, ...

MCS1721602 : A₀ = 2; A₁ = 3; A_N = A_N-1 + 2 A_N-2 (score: 5)

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

2, 3, 7, 13, 33, 71, 205, 505, 1649, 4555, 16501, 50117, 198025, 651535, 2772365, 9773041, 44357857, 166141715, 798441445, 3156692605, 15968828921, 66290544727, 351314236285, ...

MCS869384 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 + K + 1 (score: 5)

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