Minimally Complex Sequences

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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, 17, -43, 135, -388, 1349, -4269, 16187, -55498, 226617, -832471, 3625871, -14152008, 65265677, -268888153, 1305313539, -5646651214, 28716897857, -129872977923, 689205548567, ...

MCS876582 : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 - 1 (score: 4)

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

MCS13504 : A₀ = 0; A₁ = 1; A_K+1 = - A_K + K A_K-1 (score: 4)

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

MCS3442726 : A₀ = 1; A₁ = 1; A_K+1 = A_K + K A_K-1 + A_K-1 (score: 5)

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

MCS13440 : 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, -6, 31, -156, 973, -6960, 56661, -516900, 5225671, -57999270, 701216923, -9173819256, 129134686521, ...

MCS13385 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K + A_K-1 + K (score: 5)

3, 7, 6, -2, -7, 5, 28, 28, -17, -61, -14, 122, 165, -63, -376, -232, 539, 1023, -34, -2058, -1967, 2173, 6132, 1812, -10425, -14021, 6858, 34930, 21245, -48583, -91040, 6160, 188275, 175991, ...

MCS13781766 : A₀ = 1; A₁ = 1; A_K+1 = A_K - 2 A_K-1 + K (score: 5)

3, -7, 9, -17, 25, -43, 67, -111, 177, -289, 465, -755, 1219, -1975, 3193, -5169, 8361, -13531, 21891, -35423, 57313, -92737, 150049, -242787, 392835, -635623, 1028457, -1664081, 2692537, ...

MCS3518982 : A₀ = 1; A₁ = 1; A_N = - A_N-1 + A_N-2 - 1 (score: 4)

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, -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, ...

MCS3453700 : A₀ = 1; A₁ = 3; A_N = - 2 A_N-1 - A_N-2 (score: 5)

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

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, ...

MCS7860 (alias MCS3956) : A₀ = 0; A_K+1 = A_K + K - 2 (score: 4)

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' (A77043)

3, 7, 12, 20, 28, 41, 51, 71, 80, 112, 112, 169, 139, 255, 140, 404, 60, 705, -245, 1391, -1152, 3072, -3648, 7345, -10317, 18391, -27924, 47156, -74180, 122297, -195453, 318839, -513136, 833200, ...

MCS864801 : A₀ = 0; A₁ = 0; A_K+1 = - A_K + A_K-1 + K² (score: 5)

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 (A2061)

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, ...

MCS505219 : A₀ = 3; A_N = - 2 A_N-1 - 1 (score: 5)

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, ...

MCS13541 : A₀ = 0; A₁ = 1; A_N = 3 A_N-1 - 2 A_N-2 (score: 6)

2^N-1 (A0225)

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

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 (A0225)

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

MCS809009 : A₀ = 0; 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, ...

MCS3453446 : A₀ = 1; A₁ = 1; A_N = - 2 A_N-1 + A_N-2 (score: 4)

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

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, 23, 45, 85, 137, 213, 307, 431, 579, 763, 977, 1233, 1525, 1865, 2247, 2683, 3167, 3711, 4309, 4973, 5697, 6493, 7355, 8295, 9307, 10403, 11577, 12841, 14189, 15633, 17167, 18803, 20535, ...

MCS124548 : A₀ = 1; A_K+1 = - A_K + K³ + K (score: 5)

3, -7, 23, -71, 275, -995, 4399, -17911, 87979, -394043, 2111495, -10245119, 59121859, -307353571, 1891899487, -10450021415, 68108381531, -397100813771, ...

MCS54786 : A₀ = 0; A₁ = 1; A_K+1 = 2 K A_K-1 - 1 (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, 25, -118, 683, -4663, 36621, -324926, 3212639, -35014103, 416956597, -5385421658, 74978946615, ...

MCS855430 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K - A_K-1 (score: 4)

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, -7, 31, -151, 911, -6371, 50975, -458767, 4587679, -50464459, 605573519, -7872455735, 110214380303, ...

MCS124568 : A₀ = 1; A_K+1 = - K A_K - A_K + K (score: 4)

3, 8, -3, -19, -2, 41, 23, -80, -87, 137, 254, -187, -645, 120, 1477, 405, -3074, -2287, 5743, 7648, -9199, -21039, 10750, 51277, -461, -113304, -50355, 227069, 214014, -403783, -655097, 593552, ...

MCS792113 : A₀ = 0; A₁ = 1; A₂ = 1; A_N = - 2 A_N-2 - A_N-3 (score: 5)

3, 8, -4, -27, -27, 18, 62, 15, -121, -164, 64, 377, 233, -538, -1022, 35, 2059, 1968, -2172, -6131, -1811, 10426, 14022, -6857, -34929, -21244, 48584, 91041, -6159, -188274, -175990, 200523, ...

MCS13789958 : A₀ = 1; A₁ = 1; A_K+1 = A_K - 2 A_K-1 - K (score: 5)

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, 13, -30, 55, -116, 225, -458, 907, -1824, 3637, -7286, 14559, -29132, 58249, -116514, 233011, -466040, 932061, -1864142, 3728263, -7456548, 14913073, -29826170, 59652315, -119304656, ...

MCS124336 (alias MCS13746, MCS15661, MCS1004976, MCS7038214)

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

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, MCS7062, MCS7890, MCS500897)

A_K = K² - 1 (score: 3)

N²-1, or (N+1)(N-1) (A5563)

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

MCS213046 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K-1 (score: 3)

3, 8, 17, 32, 57, 100, 177, 320, 593, 1124, 2169, 4240, 8361, 16580, 32993, 65792, 131361, 262468, 524649, 1048976, 2097593, 4194788, 8389137, 16777792, 33555057, 67109540, 134218457, 268436240, ...

MCS2004300 : A₀ = 1; A_K+1 = 2 A_K - K² + 2 K + 1 (score: 7)

2^N+N² (A1580)

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 (A1906)

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

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, -30, 231, 40, -2349, 1910, 26279, -51108, -316797, 1083418, 3985335, -22403440, -49332589, 474997950, 511653831, -10486610780, -769773501, 241961821442, -223487257417, ...

MCS871437 : A₀ = 0; A₁ = 0; A_K+1 = - A_K - K A_K-1 + 1 (score: 5)

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, -75, 229, -682, 2052, -6149, 18455, -55356, 166078, -498223, 1494681, -4484030, 13452104, -40356297, 121068907, -363206704, 1089620130, -3268860371, 9806581133, -29419743378, ...

MCS15806 (alias MCS499521) : A₀ = 0; A_K+1 = - 3 A_K + 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, -8, 45, -264, 1855, -14832, 133497, -1334960, 14684571, -176214840, 2290792933, -32071101048, 481066515735, ...

MCS31337 : A₀ = 0; A_K+1 = - K A_K - A_K + K + 1 (score: 5)

3, -8, 45, -264, 1855, -14832, 133497, -1334960, 14684571, -176214840, 2290792933, -32071101048, 481066515735, ...

MCS31561 (alias MCS504984) : A₀ = 0; A_K+1 = - K A_K + A_K + K - 1 (score: 5)

3, -8, 45, -264, 1855, -14832, 133497, -1334960, 14684571, -176214840, 2290792933, -32071101048, 481066515735, ...

MCS1929 (alias MCS30872, MCS61745) : A₀ = 0; A_K+1 = - K A_K + K (score: 3)

3, -9, 7, -18, 18, -35, 42, -72, 94, -150, 207, -317, 450, -675, 973, -1443, 2097, -3092, 4512, -6633, 9700, -14238, 20844, -30572, 44781, -65655, 96196, -141009, 206631, -302861, 443835, -650502, ...

MCS1628257 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = - A_K - A_K-2 - K (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, 15, -33, 63, -129, 255, -513, 1023, -2049, 4095, -8193, 16383, -32769, 65535, -131073, 262143, -524289, 1048575, -2097153, 4194303, -8388609, 16777215, -33554433, 67108863, -134217729, ...

MCS15861 : A₀ = 0; A_N = - 2 A_N-1 - 3 (score: 5)

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)

3, 9, 19, 34, 55, 83, 119, 164, 219, 285, 363, 454, 559, 679, 815, 968, 1139, 1329, 1539, 1770, 2023, 2299, 2599, 2924, 3275, 3653, 4059, 4494, 4959, 5455, 5983, 6544, 7139, 7769, 8435, 9138, ...

MCS1708301 : A₀ = -1; A₁ = -1; A_K+1 = A_K-1 + K² (score: 5)

3, 9, 21, 41, 71, 113, 169, 241, 331, 441, 573, 729, 911, 1121, 1361, 1633, 1939, 2281, 2661, 3081, 3543, 4049, 4601, 5201, 5851, 6553, 7309, 8121, 8991, 9921, 10913, 11969, 13091, 14281, 15541, ...

MCS124040 (alias MCS124104, MCS1708358) : A₀ = 1; A_K+1 = A_K + K² + K (score: 4)

3, 9, 21, 45, 93, 189, 381, 765, 1533, 3069, 6141, 12285, 24573, 49149, 98301, 196605, 393213, 786429, 1572861, 3145725, 6291453, 12582909, 25165821, 50331645, 100663293, 201326589, 402653181, ...

MCS1978 : A₀ = 0; A_N = 2 A_N-1 + 3 (score: 5)

3, 9, 23, 53, 115, 241, 495, 1005, 2027, 4073, 8167, 16357, 32739, 65505, 131039, 262109, 524251, 1048537, 2097111, 4194261, 8388563, 16777169, 33554383, 67108813, 134217675, 268435401, 536870855, ...

MCS501072 (alias MCS505168) : A₀ = 1; A_K+1 = 2 A_K + 2 K + 1 (score: 5)

3, 9, 24, 61, 151, 369, 896, 2169, 5243, 12665, 30584, 73845, 178287, 430433, 1039168, 2508785, 6056755, 14622313, 35301400, 85225133, 205751687, 496728529, 1199208768, 2895146089, 6989500971, ...

MCS6740 : A₀ = 0; A₁ = 1; A_K+1 = 2 A_K + A_K-1 + K (score: 5)

3, 9, 25, 75, 231, 763, 2619, 9495, 35695, 140151, 568503, 2390479, 10349535, 46206735, 211799311, 997313823, 4809701439, 23758664095, 119952692895, 618884638911, ...

MCS861193 : A₀ = 0; A₁ = 0; A_K+1 = A_K + K A_K-1 + K (score: 5)

3, -9, 27, -81, 243, -729, 2187, -6561, 19683, -59049, 177147, -531441, 1594323, -4782969, 14348907, -43046721, 129140163, -387420489, 1162261467, -3486784401, 10460353203, -31381059609, ...

MCS124865 (alias MCS249731) : A₀ = -1; A_N = - 3 A_N-1 (score: 4)

3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, ...

MCS15584 (alias MCS62339) : A₀ = 1; A_N = 3 A_N-1 (score: 3)

Powers of 3 (A0244)

3, -9, 29, -141, 811, -5543, 43525, -386191, 3818375, -41615945, 495572953, -6400832457, 89116081431, ...

MCS3435910 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K - A_K-1 - K (score: 5)

3, 9, 31, 129, 651, 3913, 27399, 219201, 1972819, 19728201, 217010223, 2604122689, 33853594971, 473950329609, ...

MCS3892 (alias MCS124560, MCS249121) : A₀ = 0; A_K+1 = K A_K - A_K + K (score: 4)

3, 9, 31, 129, 651, 3913, 27399, 219201, 1972819, 19728201, 217010223, 2604122689, 33853594971, 473950329609, ...

MCS3908 (alias MCS125072, MCS250145) : A₀ = 0; A_K+1 = K A_K + K + 1 (score: 4)

3, 9, 33, 145, 763, 4729, 33873, 275721, 2515371, 25429441, 282239233, 3412300249, 44642142483, 628402295025, ...

MCS3426566 : A₀ = 1; A₁ = 1; A_K+1 = K A_K + A_K-1 + K (score: 5)

3, 9, 34, 162, 939, 6412, 50358, 446811, 4417753, 48148473, 573363924, 7405582540, 103104791637, ...

MCS869185 : A₀ = 0; A₁ = 0; A_K+1 = K A_K - A_K-1 + 1 (score: 5)

3, -10, 11, -38, 51, -138, 227, -518, 955, -2010, 3899, -7942, 15715, -31626, 63027, -126310, 252331, -504986, 1009611, -2019622, 4038803, -8078090, 16155651, -32311878, 64623131, -129246938, ...

MCS124300 : A₀ = 1; A_K+1 = - 2 A_K - K² (score: 4)

3, 10, 19, 35, 55, 84, 119, 165, 219, 286, 363, 455, 559, 680, 815, 969, 1139, 1330, 1539, 1771, 2023, 2300, 2599, 2925, 3275, 3654, 4059, 4495, 4959, 5456, 5983, 6545, 7139, 7770, 8435, 9139, ...

MCS854149 : A₀ = 0; A₁ = -1; A_K+1 = A_K-1 + K² (score: 5)

3, 10, 21, 36, 55, 78, 105, 136, 171, 210, 253, 300, 351, 406, 465, 528, 595, 666, 741, 820, 903, 990, 1081, 1176, 1275, 1378, 1485, 1596, 1711, 1830, 1953, 2080, 2211, 2346, 2485, 2628, 2775, ...

MCS7058 : A_K = 2 K² + K (score: 4)

3, -10, 21, -72, 197, -702, 2277, -8596, 31365, -125922, 502301, -2139288, 9171501, -41260822, 188004837, -889438812, 4273525877, -21172863306, 106643380845, -551273510272, ...

MCS54976 : A₀ = 0; A₁ = 1; A_K+1 = - A_K + K A_K-1 - 1 (score: 5)

3, 10, 25, 56, 119, 246, 501, 1012, 2035, 4082, 8177, 16368, 32751, 65518, 131053, 262124, 524267, 1048554, 2097129, 4194280, 8388583, 16777190, 33554405, 67108836, 134217699, 268435426, ...

MCS501057 : A₀ = -1; A_K+1 = 2 A_K + K + 1 (score: 5)

3, -10, 28, -87, 257, -776, 2322, -6973, 20911, -62742, 188216, -564659, 1693965, -5081908, 15245710, -45737145, 137211419, -411634274, 1234902804, -3704708431, 11114125273, -33342375840, ...

MCS499553 : A₀ = -1; A_K+1 = - 3 A_K - K (score: 5)

3, 10, 32, 99, 301, 908, 2730, 8197, 24599, 73806, 221428, 664295, 1992897, 5978704, 17936126, 53808393, 161425195, 484275602, 1452826824, 4358480491, 13075441493, 39226324500, 117678973522, ...

MCS62368 : A₀ = 1; A_K+1 = 3 A_K + K (score: 4)

3, 10, 33, 109, 360, 1189, 3927, 12970, 42837, 141481, 467280, 1543321, 5097243, 16835050, 55602393, 183642229, 606529080, 2003229469, 6616217487, 21851881930, 72171863277, 238367471761, ...

MCS1692 : A₀ = 0; A₁ = 1; A_N = 3 A_N-1 + A_N-2 (score: 5)

Value of Fibonacci polynomials when x=3 (A6190)

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

3, 10, 34, 111, 349, 1072, 3252, 9805, 29479, 88518, 265654, 797083, 2391393, 7174348, 21523240, 64569945, 193710091, 581130562, 1743392010, 5230176391, 15690529573, 47071589160, 141214767964, ...

MCS62344 : A₀ = 1; A_K+1 = 3 A_K + K² (score: 5)

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

MCS126360 : A₀ = 1; A_K+1 = - K A_K - A_K - 1 (score: 4)

3, 10, 41, 206, 1237, 8660, 69281, 623530, 6235301, 68588312, 823059745, 10699776686, 149796873605, ...

MCS250512 : A₀ = 1; A_K+1 = K A_K + 2 A_K + 1 (score: 5)

Distinct Ordered Proper Subsets of a Set With N Elements (A2627)

3, 10, 41, 206, 1237, 8660, 69281, 623530, 6235301, 68588312, 823059745, 10699776686, 149796873605, ...

MCS3912 : A₀ = 0; A_K+1 = K A_K + A_K + 1 (score: 4)

Distinct Ordered Proper Subsets of a Set With N Elements (A2627)

3, 10, 41, 206, 1237, 8660, 69281, 623530, 6235301, 68588312, 823059745, 10699776686, 149796873605, ...

MCS217153 : A₀ = 0; A₁ = 0; A_K+1 = K A_K + 1 (score: 4)

Distinct Ordered Proper Subsets of a Set With N Elements (A2627)

3, 10, 41, 208, 1258, 8847, 70984, 640114, 6409987, 70580841, 847610206, 11025342665, 154425378151, ...

MCS6308918 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = K A_K + A_K-2 (score: 5)

3, -10, 43, -225, 1393, -9976, 81201, -740785, 7489051, -83120346, 1004933203, -13147251985, 185066460993, ...

MCS3337 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K + A_K-1 (score: 4)

3, 10, 43, 225, 1393, 9976, 81201, 740785, 7489051, 83120346, 1004933203, 13147251985, 185066460993, ...

MCS1668 : A₀ = 0; A₁ = 1; A_K+1 = K A_K + A_K-1 (score: 4)

3, 10, 43, 225, 1393, 9976, 81201, 740785, 7489051, 83120346, 1004933203, 13147251985, 185066460993, ...

MCS3442950 : A₀ = 1; A₁ = 1; A_K+1 = K A_K + A_K + A_K-1 (score: 5)

3, -10, 48, -277, 1892, -14858, 131831, -1303451, 14206131, -169170120, 2185005430, -30420905899, 454128583056, ...

MCS869217 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K - A_K-1 + 1 (score: 5)

3, -10, 63, -424, 3337, -29600, 292673, -3189792, 37984843, -490613154, 6830599327, -101968376736, ...

MCS13389 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K - A_K-1 + K (score: 5)

3, -11, 15, -39, 67, -147, 279, -575, 1131, -2283, 4543, -9111, 18195, -36419, 72807, -145647, 291259, -582555, 1165071, -2330183, 4660323, -9320691, 18641335, -37282719, 74565387, -149130827, ...

MCS62645 (alias MCS2021040) : A₀ = 0; A_K+1 = - 2 A_K - 2 K + 1 (score: 5)

3, -11, 21, -58, 131, -327, 777, -1890, 4547, -10995, 26525, -64058, 154627, -373327, 901265, -2175874, 5252995, -12681883, 30616741, -73915386, 178447491, -430810391, 1040068249, -2510946914, ...

MCS13818374 : A₀ = 1; A₁ = 1; A_K+1 = - 2 A_K + A_K-1 - K (score: 5)

3, 11, 26, 50, 85, 133, 196, 276, 375, 495, 638, 806, 1001, 1225, 1480, 1768, 2091, 2451, 2850, 3290, 3773, 4301, 4876, 5500, 6175, 6903, 7686, 8526, 9425, 10385, 11408, 12496, 13651, 14875, ...

MCS126216 (alias MCS15508, MCS496328) : A₀ = 1; A_K+1 = A_K + K² - 1 (score: 4)

3, 11, 29, 61, 111, 183, 281, 409, 571, 771, 1013, 1301, 1639, 2031, 2481, 2993, 3571, 4219, 4941, 5741, 6623, 7591, 8649, 9801, 11051, 12403, 13861, 15429, 17111, 18911, 20833, 22881, 25059, ...

MCS61972 : A₀ = 1; A_K+1 = A_K + 2 K² (score: 4)

3, 11, 31, 69, 131, 223, 351, 521, 739, 1011, 1343, 1741, 2211, 2759, 3391, 4113, 4931, 5851, 6879, 8021, 9283, 10671, 12191, 13849, 15651, 17603, 19711, 21981, 24419, 27031, 29823, 32801, 35971, ...

MCS14152 : A_K = K³ + K + 1 (score: 5)

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