Munafo's Classical Sequences

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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, ...

MCS427267 : A₀ = 3; A₁ = 4; A_N = 2 A_N-2 (score: 5)

Horadam sequence W_n(3, 4; 2, 0)

3, 4, 6, 9, 11, 14, 18, 21, 25, 30, 34, 39, 45, 50, 56, 63, 69, 76, 84, 91, 99, 108, 116, 125, 135, 144, 154, 165, 175, 186, 198, 209, 221, 234, 246, 259, 273, 286, 300, 315, 329, 344, 360, 375, ...

MCS1642561 (alias MCS3179033) : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = A_K-2 + K + 1 (score: 5)

3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864, 906, ...

MCS500867 : A₀ = 3; A_K+1 = A_K + K + 1 (score: 5)

3, 4, 7, 9, 13, 16, 21, 25, 31, 36, 43, 49, 57, 64, 73, 81, 91, 100, 111, 121, 133, 144, 157, 169, 183, 196, 211, 225, 241, 256, 273, 289, 307, 324, 343, 361, 381, 400, 421, 441, 463, 484, 507, ...

MCS836 (alias MCS3478022, MCS13996550, MCS14043158)

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

N²/4, rounded up (A004652)

3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, ...

MCS860676 (alias MCS860675) : A₀ = 1; A₁ = 3; A_N = A_N-1 + A_N-2 (score: 4)

Lucas numbers (A000204)

Horadam sequence W_n(1, 3; 1, 1) ; Horadam sequence W_n(3, 4; 1, 1)

3, 4, 7, 12, 19, 28, 39, 52, 67, 84, 103, 124, 147, 172, 199, 228, 259, 292, 327, 364, 403, 444, 487, 532, 579, 628, 679, 732, 787, 844, 903, 964, 1027, 1092, 1159, 1228, 1299, 1372, 1447, 1524, ...

MCS3548 : A_K = K² + 3 (score: 5)

3, 4, 8, 10, 15, 18, 24, 28, 35, 40, 48, 54, 63, 70, 80, 88, 99, 108, 120, 130, 143, 154, 168, 180, 195, 208, 224, 238, 255, 270, 288, 304, 323, 340, 360, 378, 399, 418, 440, 460, 483, 504, 528, ...

MCS1746049 (alias MCS6852653) : A₀ = 0; A₁ = 0; A_K+1 = A_K-1 + K + 2 (score: 5)

3, 4, 9, 12, 19, 24, 33, 40, 51, 60, 73, 84, 99, 112, 129, 144, 163, 180, 201, 220, 243, 264, 289, 312, 339, 364, 393, 420, 451, 480, 513, 544, 579, 612, 649, 684, 723, 760, 801, 840, 883, 924, ...

MCS31340 (alias MCS501384, MCS6858774) : A₀ = 0; A_K+1 = - A_K + K² - K + 1 (score: 5)

3, 4, 9, 12, 23, 30, 53, 68, 115, 146, 241, 304, 495, 622, 1005, 1260, 2027, 2538, 4073, 5096, 8167, 10214, 16357, 20452, 32739, 40930, 65505, 81888, 131039, 163806, 262109, 327644, 524251, ...

MCS1713414 : A₀ = 1; A₁ = 1; A_K+1 = 2 A_K-1 + K (score: 4)

3, 4, 10, 22, 62, 172, 544, 1748, 6100, 21832, 82832, 322984, 1316968, 5515760, 23953312, 106689712, 489942704, 2303667808, 11122636480, 54892324832, 277345054432, ...

MCS860196 : A₀ = 1; A₁ = 3; A_K+1 = A_K + K A_K-1 (score: 5)

3, 4, 11, 18, 57, 110, 401, 882, 3611, 8822, 39723, 105866, 516401, 1482126, 7746017, 23714018, 131682291, 426852326, 2501963531, 8537046522, 52541234153, 187815023486, ...

MCS1744934 : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 + 2 (score: 5)

3, 4, 11, 37, 159, 832, 5151, 36889, 300263, 2739256, 27692823, 307360309, 3716016531, 48615575212, 684334069499, ...

MCS854276 : A₀ = 1; A₁ = 3; A_K+1 = K A_K + A_K-1 (score: 5)

3, 4, 13, 21, 79, 148, 633, 1333, 6331, 14664, 75973, 190633, 1063623, 2859496, 17017969, 48611433, 306323443, 923617228, 6126468861, 19395961789, 134782314943, 446107121148, ...

MCS13568 (alias MCS869129, MCS3475494) : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 + 1 (score: 4)

3, 4, 13, 23, 82, 174, 679, 1648, 6964, 18807, 85216, 251455, 1211831, 3857041, 19640751, 66781528, 357390559, 1288489783, 7214592708, 27415676002, 160009529359, 637775140754, ...

MCS6296118 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = K A_K-1 + A_K-2 (score: 5)

3, 4, 15, 24, 105, 192, 945, 1920, 10395, 23040, 135135, 322560, 2027025, 5160960, 34459425, 92897280, 654729075, 1857945600, 13749310575, 40874803200, 316234143225, 980995276800, ...

MCS1709094 : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 + 2 A_K-1 (score: 5)

3, 4, 20, 30, 147, 248, 1332, 2490, 14663, 29892, 190632, 418502, 2859495, 6696048, 48611432, 120528882, 923617227, 2410577660, 19395961788, 53032708542, 446107121147, ...

MCS1712205 : A₀ = -1; A₁ = -1; A_K+1 = K A_K-1 + K (score: 5)

3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, ...

MCS1573924 : A₀ = 1; A₁ = 3; A₂ = 5; A_N = A_N-3 (score: 5)

3, 5, 3, 3, 7, 9, 7, 7, 11, 13, 11, 11, 15, 17, 15, 15, 19, 21, 19, 19, 23, 25, 23, 23, 27, 29, 27, 27, 31, 33, 31, 31, 35, 37, 35, 35, 39, 41, 39, 39, 43, 45, 43, 43, 47, 49, 47, 47, 51, 53, 51, ...

MCS3429901 : A₀ = -1; A₁ = -1; A_K+1 = - A_K-1 + 2 K (score: 5)

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

MCS854035 : A₀ = 3; A₁ = 5; A_N = A_N-2 (score: 5)

Horadam sequence W_n(3, 5; 1, 0)

3, 5, 4, 4, 7, 9, 8, 8, 11, 13, 12, 12, 15, 17, 16, 16, 19, 21, 20, 20, 23, 25, 24, 24, 27, 29, 28, 28, 31, 33, 32, 32, 35, 37, 36, 36, 39, 41, 40, 40, 43, 45, 44, 44, 47, 49, 48, 48, 51, 53, 52, ...

MCS1739457 : A₀ = 0; A₁ = 0; A_K+1 = - A_K-1 + 2 K + 1 (score: 5)

3, 5, 5, 5, 7, 9, 9, 9, 11, 13, 13, 13, 15, 17, 17, 17, 19, 21, 21, 21, 23, 25, 25, 25, 27, 29, 29, 29, 31, 33, 33, 33, 35, 37, 37, 37, 39, 41, 41, 41, 43, 45, 45, 45, 47, 49, 49, 49, 51, 53, 53, ...

MCS1714950 : A₀ = 1; A₁ = 1; A_K+1 = - A_K-1 + 2 K (score: 4)

3, 5, 6, 6, 6, 7, 9, 11, 12, 12, 12, 13, 15, 17, 18, 18, 18, 19, 21, 23, 24, 24, 24, 25, 27, 29, 30, 30, 30, 31, 33, 35, 36, 36, 36, 37, 39, 41, 42, 42, 42, 43, 45, 47, 48, 48, 48, 49, 51, 53, 54, ...

MCS861377 (alias MCS27209, MCS3515585) : A₀ = 0; A₁ = 0; A_K+1 = A_K - A_K-1 + K (score: 4)

3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 24, 25, 27, 29, 30, 31, 33, 35, 36, 37, 39, 41, 42, 43, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 63, 65, 66, 67, 69, 71, 72, 73, 75, 77, ...

MCS3357 : A₀ = 0; A₁ = 1; A_K+1 = - A_K-1 + 3 K (score: 5)

3, 5, 6, 9, 12, 14, 18, 22, 25, 30, 35, 39, 45, 51, 56, 63, 70, 76, 84, 92, 99, 108, 117, 125, 135, 145, 154, 165, 176, 186, 198, 210, 221, 234, 247, 259, 273, 287, 300, 315, 330, 344, 360, 376, ...

MCS794753 (alias MCS821281) : A₀ = -1; A₁ = 0; A₂ = 1; A_K+1 = A_K-2 + K (score: 5)

3, 5, 7, 7, 7, 7, 9, 11, 13, 13, 13, 13, 15, 17, 19, 19, 19, 19, 21, 23, 25, 25, 25, 25, 27, 29, 31, 31, 31, 31, 33, 35, 37, 37, 37, 37, 39, 41, 43, 43, 43, 43, 45, 47, 49, 49, 49, 49, 51, 53, 55, ...

MCS12748342 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = - A_K-2 + 2 K (score: 5)

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, ...

MCS3538 (alias MCS3546, MCS7098, MCS62784, MCS125569, MCS251139, MCS1002160, MCS1725188)

A_K = 2 K + 1 (score: 3)

Odd numbers (A005408)

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

3, 5, 7, 11, 17, 25, 37, 55, 81, 119, 175, 257, 377, 553, 811, 1189, 1743, 2555, 3745, 5489, 8045, 11791, 17281, 25327, 37119, 54401, 79729, 116849, 171251, 250981, 367831, 539083, 790065, ...

MCS26346550 : A₀ = 1; A₁ = 1; A₂ = 1; A_N = A_N-1 + A_N-3 + 1 (score: 5)

3, 5, 7, 13, 23, 37, 63, 109, 183, 309, 527, 893, 1511, 2565, 4351, 7373, 12503, 21205, 35951, 60957, 103367, 175269, 297183, 503917, 854455, 1448821, 2456655, 4165565, 7063207, 11976517, ...

MCS401489 (alias MCS802977, MCS12847670) : A₀ = 0; A₁ = 1; A₂ = 1; A_N = A_N-1 + 2 A_N-3 (score: 5)

3, 5, 8, 11, 15, 19, 24, 29, 35, 41, 48, 55, 63, 71, 80, 89, 99, 109, 120, 131, 143, 155, 168, 181, 195, 209, 224, 239, 255, 271, 288, 305, 323, 341, 360, 379, 399, 419, 440, 461, 483, 505, 528, ...

MCS1713165 (alias MCS6820, MCS1739009) : A₀ = -1; A₁ = -1; A_K+1 = A_K-1 + K (score: 4)

3, 5, 8, 12, 16, 21, 27, 33, 40, 48, 56, 65, 75, 85, 96, 108, 120, 133, 147, 161, 176, 192, 208, 225, 243, 261, 280, 300, 320, 341, 363, 385, 408, 432, 456, 481, 507, 533, 560, 588, 616, 645, 675, ...

MCS865057 : A₀ = 0; A₁ = 0; A_K+1 = - A_K - A_K-1 + K² (score: 5)

3, 5, 8, 13, 19, 28, 40, 56, 78, 107, 146, 198, 267, 359, 481, 643, 858, 1143, 1521, 2022, 2686, 3566, 4732, 6277, 8324, 11036, 14629, 19389, 25695, 34049, 45116, 59777, 79199, 104928, 139012, ...

MCS795681 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = A_K-1 + A_K-2 + K (score: 5)

3, 5, 9, 13, 19, 25, 33, 41, 51, 61, 73, 85, 99, 113, 129, 145, 163, 181, 201, 221, 243, 265, 289, 313, 339, 365, 393, 421, 451, 481, 513, 545, 579, 613, 649, 685, 723, 761, 801, 841, 883, 925, ...

MCS1714694 : A₀ = 1; A₁ = 1; A_K+1 = A_K-1 + 2 K (score: 4)

3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049, 242785, 392835, 635621, 1028457, 1664079, 2692537, 4356617, 7049155, ...

MCS3482118 (alias MCS3482116) : A₀ = 1; A₁ = 1; A_N = A_N-1 + A_N-2 + 1 (score: 4)

3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201, 2209, 4063, 7473, 13745, 25281, 46499, 85525, 157305, 289329, 532159, 978793, 1800281, 3311233, 6090307, 11201821, 20603361, 37895489, 69700671, ...

MCS25723958 : A₀ = 1; A₁ = 1; A₂ = 1; A_N = A_N-1 + A_N-2 + A_N-3 (score: 5)

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, ...

MCS252547 : A₀ = 3; A_N = 2 A_N-1 - 1 (score: 5)

3, 5, 10, 14, 21, 27, 36, 44, 55, 65, 78, 90, 105, 119, 136, 152, 171, 189, 210, 230, 253, 275, 300, 324, 351, 377, 406, 434, 465, 495, 528, 560, 595, 629, 666, 702, 741, 779, 820, 860, 903, 945, ...

MCS15572 (alias MCS252689, MCS1739393) : A₀ = 0; A_K+1 = - A_K + K² + 2 K (score: 5)

3, 5, 10, 18, 32, 55, 93, 155, 256, 420, 686, 1117, 1815, 2945, 4774, 7734, 12524, 20275, 32817, 53111, 85948, 139080, 225050, 364153, 589227, 953405, 1542658, 2496090, 4038776, 6534895, 10573701, ...

MCS3445252 : A₀ = 1; A₁ = 3; A_K+1 = A_K + A_K-1 + K (score: 5)

3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971, 357913941, ...

MCS3362 (alias MCS1721604, MCS1721606) : A₀ = 0; A₁ = 1; A_N = A_N-1 + 2 A_N-2 (score: 4)

Jacobsthal sequence (A001045)

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

3, 5, 13, 25, 71, 157, 505, 1265, 4555, 12661, 50117, 151945, 651535, 2127245, 9773041, 34035937, 166141715, 612646885, 3156692605, 12252937721, 66290544727, 269564629885, ...

MCS53552 (alias MCS3427366, MCS3477542) : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 - A_K-1 + K (score: 5)

3, 5, 15, 29, 95, 209, 767, 1889, 7679, 20789, 92159, 270269, 1290239, 4054049, 20643839, 68918849, 371589119, 1309458149, 7431782399, 27498621149, 163499212799, 632468286449, ...

MCS3426342 (alias MCS3510310) : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 + A_K-1 + K (score: 5)

3, 5, 19, 41, 191, 493, 2675, 7889, 48151, 157781, 1059323, 3786745, 27542399, 106028861, 826271971, 3392923553, 28093247015, 122145247909, ...

MCS1736790 : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K-1 + 1 (score: 5)

3, 5, 21, 45, 231, 585, 3465, 9945, 65835, 208845, 1514205, 5221125, 40883535, 151412625, 1267389585, 4996616625, 44358635475, 184874815125, ...

MCS1708118 (alias MCS1710166) : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K-1 + A_K-1 (score: 5)

3, 5, 23, 49, 275, 685, 4399, 12329, 87979, 271237, 2111495, 7052161, 59121859, 211564829, 1891899487, 7193204185, 68108381531, 273341759029, ...

MCS1753174 : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K-1 - 1 (score: 5)

3, 6, 6, 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, ...

MCS62360 : A₀ = 1; A_K+1 = - K A_K + 3 A_K (score: 5)

3, 6, 6, 6, 9, 12, 12, 12, 15, 18, 18, 18, 21, 24, 24, 24, 27, 30, 30, 30, 33, 36, 36, 36, 39, 42, 42, 42, 45, 48, 48, 48, 51, 54, 54, 54, 57, 60, 60, 60, 63, 66, 66, 66, 69, 72, 72, 72, 75, 78, ...

MCS429761 : A₀ = 0; A₁ = 0; A_K+1 = - A_K-1 + 3 K (score: 5)

3, 6, 7, 6, 5, 6, 9, 12, 13, 12, 11, 12, 15, 18, 19, 18, 17, 18, 21, 24, 25, 24, 23, 24, 27, 30, 31, 30, 29, 30, 33, 36, 37, 36, 35, 36, 39, 42, 43, 42, 41, 42, 45, 48, 49, 48, 47, 48, 51, 54, 55, ...

MCS3445509 : A₀ = 0; A₁ = -1; A_K+1 = A_K - A_K-1 + K (score: 5)

3, 6, 7, 12, 17, 20, 27, 34, 39, 48, 57, 64, 75, 86, 95, 108, 121, 132, 147, 162, 175, 192, 209, 224, 243, 262, 279, 300, 321, 340, 363, 386, 407, 432, 457, 480, 507, 534, 559, 588, 617, 644, 675, ...

MCS13516 : A₀ = 0; A₁ = 1; A_K+1 = - A_K - A_K-1 + K² (score: 5)

3, 6, 9, 11, 12, 13, 15, 18, 21, 23, 24, 25, 27, 30, 33, 35, 36, 37, 39, 42, 45, 47, 48, 49, 51, 54, 57, 59, 60, 61, 63, 66, 69, 71, 72, 73, 75, 78, 81, 83, 84, 85, 87, 90, 93, 95, 96, 97, 99, ...

MCS13461 : A₀ = 0; A₁ = 1; A_K+1 = A_K - A_K-1 + 2 K (score: 5)

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, ...

MCS883 (alias MCS494) : A_K = 3 K (score: 3)

Multiples of 3 (A008585)

3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, ...

MCS484 (alias MCS1944, MCS1956, MCS6794, MCS13609, MCS126240, MCS251168, MCS1742017, MCS1755777)

A₀ = 0; A_K+1 = A_K + K (score: 2)

Triangular numbers (A000217)

3, 6, 11, 19, 31, 49, 76, 116, 175, 262, 390, 578, 854, 1259, 1853, 2724, 4001, 5873, 8617, 12639, 18534, 27174, 39837, 58396, 85596, 125460, 183884, 269509, 394999, 578914, 848455, 1243487, ...

MCS1609793 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = A_K + A_K-2 + K (score: 5)

3, 6, 11, 19, 32, 53, 87, 142, 231, 375, 608, 985, 1595, 2582, 4179, 6763, 10944, 17709, 28655, 46366, 75023, 121391, 196416, 317809, 514227, 832038, 1346267, 2178307, 3524576, 5702885, 9227463, ...

MCS6824 : A₀ = 0; A₁ = 1; A_N = A_N-1 + A_N-2 + 2 (score: 5)

3, 6, 11, 20, 37, 70, 135, 264, 521, 1034, 2059, 4108, 8205, 16398, 32783, 65552, 131089, 262162, 524307, 1048596, 2097173, 4194326, 8388631, 16777240, 33554457, 67108890, 134217755, 268435484, ...

MCS250544 (alias MCS248515) : A₀ = 1; A_K+1 = 2 A_K - K + 1 (score: 4)

3, 6, 12, 18, 27, 36, 48, 60, 75, 90, 108, 126, 147, 168, 192, 216, 243, 270, 300, 330, 363, 396, 432, 468, 507, 546, 588, 630, 675, 720, 768, 816, 867, 918, 972, 1026, 1083, 1140, 1200, 1260, ...

MCS429697 : A₀ = 0; A₁ = 0; A_K+1 = A_K-1 + 3 K (score: 5)

3, 6, 12, 22, 39, 67, 113, 188, 310, 508, 829, 1349, 2191, 3554, 5760, 9330, 15107, 24455, 39581, 64056, 103658, 167736, 271417, 439177, 710619, 1149822, 1860468, 3010318, 4870815, 7881163, ...

MCS3445254 (alias MCS13732) : A₀ = 1; A₁ = 1; A_K+1 = A_K + A_K-1 + K (score: 4)

3, 6, 12, 23, 41, 68, 106, 157, 223, 306, 408, 531, 677, 848, 1046, 1273, 1531, 1822, 2148, 2511, 2913, 3356, 3842, 4373, 4951, 5578, 6256, 6987, 7773, 8616, 9518, 10481, 11507, 12598, 13756, ...

MCS251144 : A₀ = 1; A_K+1 = A_K + K² + 2 (score: 5)

3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, ...

MCS62083 : A₀ = 3; A_N = 2 A_N-1 (score: 4)

3 Times a Power of 2 (A007283)

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

3, 6, 13, 20, 31, 42, 57, 72, 91, 110, 133, 156, 183, 210, 241, 272, 307, 342, 381, 420, 463, 506, 553, 600, 651, 702, 757, 812, 871, 930, 993, 1056, 1123, 1190, 1261, 1332, 1407, 1482, 1561, ...

MCS250644 : A₀ = 1; A_K+1 = - A_K + 2 K² + 1 (score: 5)

3, 6, 13, 23, 39, 60, 89, 125, 171, 226, 293, 371, 463, 568, 689, 825, 979, 1150, 1341, 1551, 1783, 2036, 2313, 2613, 2939, 3290, 3669, 4075, 4511, 4976, 5473, 6001, 6563, 7158, 7789, 8455, 9159, ...

MCS3475590 : A₀ = 1; A₁ = 1; A_K+1 = A_K-1 + K² + 1 (score: 5)

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, ...

MCS248451 : A₀ = 3; A_K+1 = 2 A_K + K (score: 5)

3, 6, 15, 26, 45, 68, 101, 140, 191, 250, 323, 406, 505, 616, 745, 888, 1051, 1230, 1431, 1650, 1893, 2156, 2445, 2756, 3095, 3458, 3851, 4270, 4721, 5200, 5713, 6256, 6835, 7446, 8095, 8778, ...

MCS13416 : A₀ = 0; A₁ = 1; A_K+1 = A_K-1 + K² - K (score: 5)

3, 6, 15, 28, 55, 92, 159, 248, 399, 596, 919, 1336, 2007, 2868, 4239, 5992, 8767, 12308, 17895, 25016, 36231, 50516, 72991, 101608, 146607, 203892, 293943, 408568, 588727, 818036, 1178415, ...

MCS1709190 : A₀ = 1; A₁ = 1; A_K+1 = 2 A_K-1 + K² (score: 5)

3, 6, 15, 32, 85, 204, 609, 1648, 5499, 16500, 60511, 198024, 786669, 2772364, 11800065, 44357856, 200601139, 798441444, 3811421679, 15968828920, 80039855301, 351314236284, ...

MCS1714214 : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 + 2 K (score: 5)

3, 6, 15, 48, 195, 978, 5871, 41100, 328803, 2959230, 29592303, 325515336, 3906184035, 50780392458, 710925494415, ...

MCS1976 (alias MCS63248) : A₀ = 0; A_K+1 = K A_K + 3 (score: 5)

3, 6, 16, 41, 122, 369, 1224, 4177, 15194, 56965, 224100, 907681, 3820982, 16528517, 73843248, 338299521, 1593634738, 7683026117, 37962086140, 191622608481, 988826417422, ...

MCS3481638 : A₀ = 1; A₁ = 1; A_K+1 = A_K + K A_K-1 + 1 (score: 5)

3, 6, 18, 48, 156, 492, 1740, 6168, 23568, 91416, 374232, 1562640, 6801888, 30241488, 139071696, 653176992, 3156467520, 15566830368, 78696180768, 405599618496, ...

MCS13440 (alias MCS3442726) : A₀ = 0; A₁ = 1; A_K+1 = A_K + K A_K-1 (score: 4)

3, 6, 21, 52, 215, 630, 3017, 10088, 54315, 201770, 1194941, 4842492, 31068479, 135589790, 932054385, 4338873296, 31689849107, 156199438674, ...

MCS1712214 : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K-1 + K (score: 5)

3, 6, 27, 72, 405, 1296, 8505, 31104, 229635, 933120, 7577955, 33592320, 295540245, 1410877440, 13299311025, 67722117120, 678264862275, ...

MCS426102 : A₀ = 1; A₁ = 1; A_K+1 = 3 K A_K-1 (score: 5)

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, ...

MCS14187 : A_K = 4 K - 1 (score: 5)

3, 7, 11, 17, 23, 31, 39, 49, 59, 71, 83, 97, 111, 127, 143, 161, 179, 199, 219, 241, 263, 287, 311, 337, 363, 391, 419, 449, 479, 511, 543, 577, 611, 647, 683, 721, 759, 799, 839, 881, 923, 967, ...

MCS3429389 : A₀ = -1; A₁ = -1; A_K+1 = A_K-1 + 2 K (score: 5)

3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250, 273, 297, 322, 348, 375, 403, 432, 462, 493, 525, 558, 592, 627, 663, 700, 738, 777, 817, 858, 900, 943, 987, ...

MCS3956 : A₀ = 0; A_K+1 = A_K + K + 3 (score: 5)

3, 7, 12, 19, 27, 37, 48, 61, 75, 91, 108, 127, 147, 169, 192, 217, 243, 271, 300, 331, 363, 397, 432, 469, 507, 547, 588, 631, 675, 721, 768, 817, 867, 919, 972, 1027, 1083, 1141, 1200, 1261, ...

MCS1678 : A₀ = 0; A₁ = 1; A_K+1 = A_K-1 + 3 K (score: 5)

Hexagonal and Semi-Hexagonal numbers or 'three-quarter squares' (A077043)

3, 7, 12, 20, 33, 52, 80, 122, 184, 275, 409, 606, 895, 1319, 1941, 2853, 4190, 6150, 9023, 13234, 19406, 28452, 41710, 61141, 89619, 131356, 192525, 282173, 413559, 606115, 888320, 1301912, ...

MCS804897 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = A_K + A_K-2 + K (score: 5)

3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133, 157, 183, 211, 241, 273, 307, 343, 381, 421, 463, 507, 553, 601, 651, 703, 757, 813, 871, 931, 993, 1057, 1123, 1191, 1261, 1333, 1407, 1483, 1561, ...

MCS62032 (alias MCS7076, MCS7078, MCS502352)

A₀ = 1; A_K+1 = A_K + 2 K (score: 3)

Central Polygonal numbers N²-N+1 (A002061)

3, 7, 14, 22, 33, 45, 60, 76, 95, 115, 138, 162, 189, 217, 248, 280, 315, 351, 390, 430, 473, 517, 564, 612, 663, 715, 770, 826, 885, 945, 1008, 1072, 1139, 1207, 1278, 1350, 1425, 1501, 1580, ...

MCS31138 : A₀ = 0; A_K+1 = - A_K + 2 K² + K (score: 5)

3, 7, 14, 25, 41, 63, 92, 129, 175, 231, 298, 377, 469, 575, 696, 833, 987, 1159, 1350, 1561, 1793, 2047, 2324, 2625, 2951, 3303, 3682, 4089, 4525, 4991, 5488, 6017, 6579, 7175, 7806, 8473, 9177, ...

MCS13481 : A₀ = 0; A₁ = 1; A_K+1 = 2 A_K - A_K-1 + K (score: 5)

3, 7, 14, 26, 46, 79, 133, 221, 364, 596, 972, 1581, 2567, 4163, 6746, 10926, 17690, 28635, 46345, 75001, 121368, 196392, 317784, 514201, 832011, 1346239, 2178278, 3524546, 5702854, 9227431, ...

MCS861313 (alias MCS13604, MCS3515521) : A₀ = 0; A₁ = 0; A_K+1 = A_K + A_K-1 + K (score: 4)

3, 7, 15, 27, 45, 69, 101, 141, 191, 251, 323, 407, 505, 617, 745, 889, 1051, 1231, 1431, 1651, 1893, 2157, 2445, 2757, 3095, 3459, 3851, 4271, 4721, 5201, 5713, 6257, 6835, 7447, 8095, 8779, ...

MCS3426438 (alias MCS3434630) : A₀ = 1; A₁ = 1; A_K+1 = A_K-1 + K² + K (score: 5)

3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, ...

MCS978 (alias MCS62624, MCS250499) : A₀ = 0; A_N = 2 A_N-1 + 1 (score: 3)

2^N-1 (A000225)

3, 7, 15, 33, 73, 161, 355, 783, 1727, 3809, 8401, 18529, 40867, 90135, 198799, 438465, 967065, 2132929, 4704323, 10375711, 22884351, 50473025, 111321761, 245527873, 541528771, 1194379303, ...

MCS12911670 : A₀ = 1; A₁ = 1; A₂ = 1; A_N = 2 A_N-1 + A_N-3 (score: 5)

3, 7, 17, 41, 99, 239, 577, 1393, 3363, 8119, 19601, 47321, 114243, 275807, 665857, 1607521, 3880899, 9369319, 22619537, 54608393, 131836323, 318281039, 768398401, 1855077841, 4478554083, ...

MCS1724934 (alias MCS1724932) : A₀ = 1; A₁ = 1; A_N = 2 A_N-1 + A_N-2 (score: 4)

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

3, 7, 17, 45, 127, 371, 1101, 3289, 9851, 29535, 88585, 265733, 797175, 2391499, 7174469, 21523377, 64570099, 193710263, 581130753, 1743392221, 5230176623, 15690529827, 47071589437, 141214768265, ...

MCS249520 : A₀ = 1; A_K+1 = 3 A_K - 2 K (score: 5)

3, 7, 19, 51, 151, 463, 1527, 5239, 18991, 71391, 280303, 1137007, 4780959, 20699071, 92413471, 423598623, 1994627647, 9619402879, 47517328191, 239905385791, ...

MCS3444774 : A₀ = 1; A₁ = 1; A_K+1 = A_K + K A_K-1 + K (score: 5)

3, 7, 25, 81, 331, 1303, 5937, 26785, 133651, 669351, 3609673, 19674097, 113525595, 664400311, 4070168161, 25330978113, 163716695587, ...

MCS1720406 : A₀ = 1; A₁ = 1; A_K+1 = A_K + 2 K A_K-1 (score: 5)

3, 7, 27, 143, 1011, 9111, 100235, 1303071, 19546083, 332283431, 6313385211, 132581089455, ...

MCS8041809 : A₀ = -1; A_K+1 = 2 K A_K - A_K + 2 K + 2 (score: 9)

Rilybeast Breeding numbers (MCS01)

3, 8, 12, 16, 23, 32, 40, 48, 59, 72, 84, 96, 111, 128, 144, 160, 179, 200, 220, 240, 263, 288, 312, 336, 363, 392, 420, 448, 479, 512, 544, 576, 611, 648, 684, 720, 759, 800, 840, 880, 923, 968, ...

MCS877345 : A₀ = 0; A₁ = 0; A_K+1 = - A_K-1 + K² - 1 (score: 5)

3, 8, 13, 17, 23, 32, 41, 49, 59, 72, 85, 97, 111, 128, 145, 161, 179, 200, 221, 241, 263, 288, 313, 337, 363, 392, 421, 449, 479, 512, 545, 577, 611, 648, 685, 721, 759, 800, 841, 881, 923, 968, ...

MCS3340 : A₀ = 0; A₁ = 1; A_K+1 = - A_K-1 + K² (score: 4)

3, 8, 15, 22, 28, 34, 42, 53, 66, 79, 91, 103, 117, 134, 153, 172, 190, 208, 228, 251, 276, 301, 325, 349, 375, 404, 435, 466, 496, 526, 558, 593, 630, 667, 703, 739, 777, 818, 861, 904, 946, 988, ...

MCS6301238 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = - A_K-2 + K² (score: 5)

3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 399, 440, 483, 528, 575, 624, 675, 728, 783, 840, 899, 960, 1023, 1088, 1155, 1224, 1295, 1368, 1443, 1520, 1599, ...

MCS1772 (alias MCS3530, MCS500897) : A_K = K² - 1 (score: 3)

N²-1, or (N+1)(N-1) (A005563)

3, 8, 17, 33, 60, 105, 179, 300, 497, 817, 1336, 2177, 3539, 5744, 9313, 15089, 24436, 39561, 64035, 103636, 167713, 271393, 439152, 710593, 1149795, 1860440, 3010289, 4870785, 7881132, 12751977, ...

MCS6730 : A₀ = 0; A₁ = 1; A_K+1 = A_K + A_K-1 + 2 K (score: 5)

3, 8, 18, 32, 53, 80, 116, 160, 215, 280, 358, 448, 553, 672, 808, 960, 1131, 1320, 1530, 1760, 2013, 2288, 2588, 2912, 3263, 3640, 4046, 4480, 4945, 5440, 5968, 6528, 7123, 7752, 8418, 9120, ...

MCS877089 : A₀ = 0; A₁ = 0; A_K+1 = A_K-1 + K² - 1 (score: 5)

3, 8, 18, 35, 61, 98, 148, 213, 295, 396, 518, 663, 833, 1030, 1256, 1513, 1803, 2128, 2490, 2891, 3333, 3818, 4348, 4925, 5551, 6228, 6958, 7743, 8585, 9486, 10448, 11473, 12563, 13720, 14946, ...

MCS7824 : A₀ = 0; A_K+1 = A_K + K² + 1 (score: 4)

3, 8, 18, 39, 81, 166, 336, 677, 1359, 2724, 5454, 10915, 21837, 43682, 87372, 174753, 349515, 699040, 1398090, 2796191, 5592393, 11184798, 22369608, 44739229, 89478471, 178956956, 357913926, ...

MCS1722689 : A₀ = 0; A₁ = 0; A_K+1 = A_K + 2 A_K-1 + K (score: 5)

3, 8, 19, 42, 89, 184, 375, 758, 1525, 3060, 6131, 12274, 24561, 49136, 98287, 196590, 393197, 786412, 1572843, 3145706, 6291433, 12582888, 25165799, 50331622, 100663269, 201326564, 402653155, ...

MCS250528 : A₀ = 1; A_K+1 = 2 A_K + K + 1 (score: 4)

3, 8, 20, 44, 89, 169, 307, 540, 928, 1568, 2617, 4329, 7115, 11640, 18980, 30876, 50145, 81345, 131851, 213596, 345888, 559968, 906385, 1466929, 2373939, 3841544, 6216212, 10058540, 16275593, ...

MCS3442822 : A₀ = 1; A₁ = 1; A_K+1 = A_K + A_K-1 + K² (score: 5)

3, 8, 20, 49, 119, 288, 696, 1681, 4059, 9800, 23660, 57121, 137903, 332928, 803760, 1940449, 4684659, 11309768, 27304196, 65918161, 159140519, 384199200, 927538920, 2239277041, 5406093003, ...

MCS6804 (alias MCS1741953) : A₀ = 0; A₁ = 1; A_N = 2 A_N-1 + A_N-2 + 1 (score: 5)

3, 8, 20, 51, 137, 386, 1122, 3317, 9887, 29580, 88640, 265799, 797253, 2391590, 7174574, 21523497, 64570235, 193710416, 581130924, 1743392411, 5230176833, 15690530058, 47071589690, 141214768541, ...

MCS62348 : A₀ = 1; A_K+1 = 3 A_K - K² (score: 5)

3, 8, 21, 52, 121, 268, 573, 1196, 2457, 4996, 10093, 20308, 40761, 81692, 163581, 327388, 655033, 1310356, 2621037, 5242436, 10485273, 20970988, 41942461, 83885452, 167771481, 335543588, ...

MCS250504 : A₀ = 1; A_K+1 = 2 A_K + K² + 1 (score: 5)

3, 8, 21, 55, 144, 377, 987, 2584, 6765, 17711, 46368, 121393, 317811, 832040, 2178309, 5702887, 14930352, 39088169, 102334155, 267914296, 701408733, 1836311903, 4807526976, 12586269025, ...

MCS3385 : A₀ = 0; A₁ = 1; A_N = 3 A_N-1 - A_N-2 (score: 5)

Even-numbered Fibonacci numbers (A001906)

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

3, 8, 22, 63, 185, 550, 1644, 4925, 14767, 44292, 132866, 398587, 1195749, 3587234, 10761688, 32285049, 96855131, 290565376, 871696110, 2615088311, 7845264913, 23535794718, 70607384132, ...

MCS62384 (alias MCS7837) : A₀ = 1; A_K+1 = 3 A_K - K (score: 4)

3, 8, 25, 82, 289, 1070, 4163, 16886, 71239, 311338, 1406305, 6548666, 31379297, 154439918, 779569291, 4030177270, 21313032487, 115169255834, 635286128921, ...

MCS1724454 : A₀ = 1; A₁ = 1; A_K+1 = 2 A_K + K A_K-1 (score: 5)

3, 8, 26, 106, 532, 3194, 22360, 178882, 1609940, 16099402, 177093424, 2125121090, 27626574172, 386772038410, ...

MCS251152 : A₀ = 1; A_K+1 = K A_K + A_K + 2 (score: 5)

3, 8, 28, 121, 634, 3926, 28117, 228863, 2087885, 21107714, 234272740, 2832380595, 37055220476, 521605467260, ...

MCS3475718 : A₀ = 1; A₁ = 1; A_K+1 = K A_K + A_K-1 + 1 (score: 5)

3, 8, 30, 136, 740, 4712, 34464, 285136, 2635152, 26921792, 301410016, 3670763776, 48322749120, 683860015232, ...

MCS1709318 : A₀ = 1; A₁ = 1; A_K+1 = K A_K + 2 A_K-1 (score: 5)

3, 9, 13, 16, 23, 33, 41, 48, 59, 73, 85, 96, 111, 129, 145, 160, 179, 201, 221, 240, 263, 289, 313, 336, 363, 393, 421, 448, 479, 513, 545, 576, 611, 649, 685, 720, 759, 801, 841, 880, 923, 969, ...

MCS855174 : A₀ = 1; A₁ = 1; A_K+1 = - A_K-1 + K² (score: 4)

3, 9, 18, 30, 45, 63, 84, 108, 135, 165, 198, 234, 273, 315, 360, 408, 459, 513, 570, 630, 693, 759, 828, 900, 975, 1053, 1134, 1218, 1305, 1395, 1488, 1584, 1683, 1785, 1890, 1998, 2109, 2223, ...

MCS1939 (alias MCS7779) : A₀ = 0; A_K+1 = A_K + 3 K (score: 4)

3, 9, 19, 33, 51, 73, 99, 129, 163, 201, 243, 289, 339, 393, 451, 513, 579, 649, 723, 801, 883, 969, 1059, 1153, 1251, 1353, 1459, 1569, 1683, 1801, 1923, 2049, 2179, 2313, 2451, 2593, 2739, 2889, ...

MCS7074 : A_K = 2 K² + 1 (score: 4)

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