Minimally Complex Sequences  


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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; AK+1 = AK-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; AK+1 = 2 AK-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; AK+1 = K AK-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; AK+1 = K AK + 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; AK+1 = AK + K AK-1 + 1 (score: 5)

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

Central Polygonal numbers N2-N+1 (A2061)

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; AK+1 = - AK + 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; AK+1 = 2 AK - AK-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; AK+1 = AK + AK-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; AK+1 = AK-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; AN = 3 AN-1 - 2 AN-2 (score: 6)

2N-1 (A0225)

Horadam sequence Wn(0, 1; -2, 3), Lucas sequence Un(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; AN = 2 AN-1 + 1 (score: 3)

2N-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; AN = 2 AN-1 + AN-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; AN = 2 AN-1 + AN-2 (score: 4)

Horadam sequence Wn(1, 1; 1, 2) ; Horadam sequence Wn(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; AK+1 = 3 AK - 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; AK+1 = AK + K AK-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; AK+1 = - AK + K3 + 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; AK+1 = AK + 2 K AK-1 (score: 5)

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

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

Rilybeast Breeding numbers (MCS01)

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; AN = - 2 AN-2 - AN-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; AK+1 = AK - 2 AK-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; AK+1 = - AK-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; AK+1 = - AK-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; AK+1 = - AK-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)

AK = K2 - 1 (score: 3)

N2-1, or (N+1)(N-1) (A5563)

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; AK+1 = 2 AK - K2 + 2 K + 1 (score: 7)

2N+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; AK+1 = AK + AK-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; AK+1 = AK-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; AK+1 = AK + 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; AK+1 = AK + 2 AK-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; AK+1 = 2 AK + 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; AK+1 = AK + AK-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; AN = 2 AN-1 + AN-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; AK+1 = 3 AK - 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; AK+1 = 2 AK + 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; AN = 3 AN-1 - AN-2 (score: 5)

Even-numbered Fibonacci numbers (A1906)

Horadam sequence Wn(0, 1; -1, 3), Lucas sequence Un(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; AK+1 = 3 AK - 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; AK+1 = 2 AK + K AK-1 (score: 5)

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

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

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

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

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

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

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; AK+1 = - K AK-1 (score: 3)

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; AK+1 = - AK - K AK-1 + 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; AK+1 = - AK-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; AK+1 = AK + 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 : AK = 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; AK+1 = AK-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; AK+1 = AK + 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; AN = 2 AN-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; AK+1 = 2 AK + 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; AK+1 = 2 AK + AK-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; AK+1 = AK + K AK-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, 94143178827, ...

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

Powers of 3 (A0244)

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

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

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

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

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

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

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

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

3, -1, 0, 2, -2, -1, 1, -3, -2, 0, -4, -3, -1, -5, -4, -2, -6, -5, -3, -7, -6, -4, -8, -7, -5, -9, -8, -6, -10, -9, -7, -11, -10, -8, -12, -11, -9, -13, -12, -10, -14, -13, -11, -15, -14, -12, ...

MCS104464 : A0 = 0; A1 = 1; A2 = 3; AN = AN-3 - 1 (score: 5)

3, -1, 0, -1, 2, -9, 44, -265, 1854, -14833, 133496, -1334961, 14684570, -176214841, 2290792932, -32071101049, 481066515734, ...

MCS126051 : A0 = 3; AK+1 = - K AK - 1 (score: 5)

3, -1, 0, -5, -5, -11, -12, -19, -21, -29, -32, -41, -45, -55, -60, -71, -77, -89, -96, -109, -117, -131, -140, -155, -165, -181, -192, -209, -221, -239, -252, -271, -285, -305, -320, -341, -357, ...

MCS3512836 : A0 = 1; A1 = 3; AK+1 = AK-1 - K - 1 (score: 5)

3, -1, 1, -3, -1, -5, -3, -7, -5, -9, -7, -11, -9, -13, -11, -15, -13, -17, -15, -19, -17, -21, -19, -23, -21, -25, -23, -27, -25, -29, -27, -31, -29, -33, -31, -35, -33, -37, -35, -39, -37, -41, ...

MCS3498500 : A0 = 1; A1 = 3; AN = AN-2 - 2 (score: 5)

3, -1, 1, -4, -3, -9, -9, -16, -17, -25, -27, -36, -39, -49, -53, -64, -69, -81, -87, -100, -107, -121, -129, -144, -153, -169, -179, -196, -207, -225, -237, -256, -269, -289, -303, -324, -339, ...

MCS429314 : A0 = 0; A1 = 3; AK+1 = AK-1 - K (score: 5)

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

MCS7917 (alias MCS438530) : A0 = 0; AK+1 = - AK - K + 3 (score: 5)

3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, 3, -1, ...

MCS125633 (alias MCS251267) : A0 = -1; AN = - AN-1 + 2 (score: 4)

3, -1, 3, -9, 11, -17, 35, -57, 91, -161, 275, -457, 779, -1329, 2243, -3801, 6459, -10945, 18547, -31465, 53355, -90449, 153379, -260089, 440987, -747745, 1267923, -2149897, 3645387, -6181233, ...

MCS811185 : A0 = 0; A1 = 1; A2 = 1; AN = - AN-1 - 2 AN-3 (score: 5)

3, -1, 5, 1, 7, 3, 9, 5, 11, 7, 13, 9, 15, 11, 17, 13, 19, 15, 21, 17, 23, 19, 25, 21, 27, 23, 29, 25, 31, 27, 33, 29, 35, 31, 37, 33, 39, 35, 41, 37, 43, 39, 45, 41, 47, 43, 49, 45, 51, 47, 53, ...

MCS1006416 : A0 = 1; AK+1 = - AK + 2 K - 2 (score: 5)

3, -1, 5, -5, 11, -15, 27, -41, 69, -109, 179, -287, 467, -753, 1221, -1973, 3195, -5167, 8363, -13529, 21893, -35421, 57315, -92735, 150051, -242785, 392837, -635621, 1028459, -1664079, 2692539, ...

MCS3486212 : A0 = 1; A1 = 3; AN = - AN-1 + AN-2 + 1 (score: 5)

3, -1, 6, -4, 14, -13, 33, -39, 80, -110, 200, -299, 511, -797, 1322, -2104, 3442, -5529, 8989, -14499, 23508, -37986, 61516, -99479, 161019, -260473, 421518, -681964, 1103510, -1785445, 2888985, ...

MCS3461636 : A0 = 1; A1 = 3; AK+1 = - AK + AK-1 + K (score: 5)

3, -1, 7, -1, 15, -1, 31, -1, 63, -1, 127, -1, 255, -1, 511, -1, 1023, -1, 2047, -1, 4095, -1, 8191, -1, 16383, -1, 32767, -1, 65535, -1, 131071, -1, 262143, -1, 524287, -1, 1048575, -1, 2097151, ...

MCS868993 (alias MCS1737989) : A0 = -1; A1 = 0; AN = 2 AN-2 + 1 (score: 5)

3, -1, 7, -9, 23, -41, 87, -169, 343, -681, 1367, -2729, 5463, -10921, 21847, -43689, 87383, -174761, 349527, -699049, 1398103, -2796201, 5592407, -11184809, 22369623, -44739241, 89478487, ...

MCS1729796 : A0 = 1; A1 = 3; AN = - AN-1 + 2 AN-2 (score: 5)

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

3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, ...

MCS6972941 : A0 = -1; A1 = -1; AN = - AN-1 - AN-2 + 1 (score: 5)

3, -1, -1, 7, -9, 7, 7, -25, 39, -25, -25, 103, -153, 103, 103, -409, 615, -409, -409, 1639, -2457, 1639, 1639, -6553, 9831, -6553, -6553, 26215, -39321, 26215, 26215, -104857, 157287, -104857, ...

MCS405585 : A0 = 0; A1 = 1; A2 = 1; AN = - AN-1 + 2 AN-3 (score: 5)

3, -1, -1, -3, 1, 1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -3, 1, 1, 3, -1, ...

MCS1574438 : A0 = 1; A1 = 1; A2 = 3; AN = - AN-3 (score: 4)

3, -1, -1, -7, -9, -17, -21, -31, -37, -49, -57, -71, -81, -97, -109, -127, -141, -161, -177, -199, -217, -241, -261, -287, -309, -337, -361, -391, -417, -449, -477, -511, -541, -577, -609, -647, ...

MCS3430916 : A0 = 1; A1 = 3; AK+1 = AK-1 - 2 K (score: 5)

3, -1, -2, 3, 5, 1, 0, 5, 7, 3, 2, 7, 9, 5, 4, 9, 11, 7, 6, 11, 13, 9, 8, 13, 15, 11, 10, 15, 17, 13, 12, 17, 19, 15, 14, 19, 21, 17, 16, 21, 23, 19, 18, 23, 25, 21, 20, 25, 27, 23, 22, 27, 29, ...

MCS3511044 : A0 = 1; A1 = 3; AK+1 = - AK-1 + K - 1 (score: 5)

3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, ...

MCS6920237 : A0 = -1; A1 = -2; AN = - AN-1 - AN-2 (score: 5)

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

3, -1, -2, 4, 1, -6, 3, 7, -9, -4, 16, -5, -20, 21, 15, -41, 6, 56, -47, -50, 103, 3, -153, 100, 156, -253, -56, 409, -197, -465, 606, 268, -1071, 338, 1339, -1409, -1001, 2748, -408, -3749, 3156, ...

MCS99088 : A0 = 0; A1 = 1; A2 = 3; AN = - AN-2 + AN-3 (score: 5)

3, -1, -2, -1, -6, -8, -8, -14, -17, -18, -25, -29, -31, -39, -44, -47, -56, -62, -66, -76, -83, -88, -99, -107, -113, -125, -134, -141, -154, -164, -172, -186, -197, -206, -221, -233, -243, -259, ...

MCS6390822 : A0 = 1; A1 = 1; A2 = 3; AK+1 = AK-2 - K (score: 5)

3, -1, -2, -4, 0, 1, 3, -1, -2, -4, 0, 1, 3, -1, -2, -4, 0, 1, 3, -1, -2, -4, 0, 1, 3, -1, -2, -4, 0, 1, 3, -1, -2, -4, 0, 1, 3, -1, -2, -4, 0, 1, 3, -1, -2, -4, 0, 1, 3, -1, -2, -4, 0, 1, 3, -1, ...

MCS104472 : A0 = 0; A1 = 1; A2 = 3; AN = - AN-3 - 1 (score: 5)

3, -1, -2, -5, -16, -65, -326, -1957, -13700, -109601, -986410, -9864101, -108505112, -1302061345, -16926797486, -236975164805, ...

MCS126019 : A0 = 3; AK+1 = K AK - 1 (score: 5)

3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, 3, -1, -3, 1, ...

MCS213764 : A0 = 1; A1 = 3; AN = - AN-2 (score: 3)

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

3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, 3, -1, -4, 0, ...

MCS438658 : A0 = 0; A1 = 3; AN = - AN-2 - 1 (score: 5)

3, -1, -4, 5, 12, -5, -18, 17, 44, -25, -78, 61, 168, -109, -322, 233, 660, -449, -1302, 917, 2624, -1813, -5226, 3649, 10476, -7273, -20926, 14573, 41880, -29117, -83730, 58265, 167492, -116497, ...

MCS3427076 : A0 = 1; A1 = 3; AK+1 = - 2 AK-1 + K (score: 5)

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

MCS3480324 : A0 = 1; A1 = 3; AK+1 = - AK-1 - K + 1 (score: 5)

3, -1, -4, -2, 5, 6, -3, -11, -3, 14, 14, -11, -28, -3, 39, 31, -36, -70, 5, 106, 65, -111, -171, 46, 282, 125, -328, -407, 203, 735, 204, -938, -939, 734, 1877, 205, -2611, -2082, 2406, 4693, ...

MCS99096 : A0 = 0; A1 = 1; A2 = 3; AN = - AN-2 - AN-3 (score: 5)

3, -1, -5, 3, 11, -5, -21, 11, 43, -21, -85, 43, 171, -85, -341, 171, 683, -341, -1365, 683, 2731, -1365, -5461, 2731, 10923, -5461, -21845, 10923, 43691, -21845, -87381, 43691, 174763, -87381, ...

MCS3476228 (alias MCS3476229, MCS13904918) : A0 = 1; A1 = 3; AN = - 2 AN-2 + 1 (score: 5)

3, -1, -5, 7, 3, -17, 11, 23, -45, -1, 91, -89, -93, 271, -85, -457, 627, 287, -1541, 967, 2115, -4049, -181, 8279, -7917, -8641, 24475, -7193, -41757, 56143, 27371, -139657, 84915, 194399, ...

MCS6757 (alias MCS6919693) : A0 = 0; A1 = 1; AN = - AN-1 - 2 AN-2 (score: 4)

A1607

Horadam sequence Wn(0, 1; -2, -1), Lucas sequence Un(-1, 2) ; Horadam sequence Wn(-1, -1; -2, -1)

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

MCS429442 : A0 = 0; A1 = 3; AK+1 = - AK-1 - K (score: 5)

3, -1, -6, 3, 24, -15, -144, 105, 1152, -945, -11520, 10395, 138240, -135135, -1935360, 2027025, 30965760, -34459425, -557383680, 654729075, 11147673600, -13749310575, -245248819200, 316234143225, ...

MCS213044 : A0 = 1; A1 = 3; AK+1 = - K AK-1 (score: 4)

3, -1, 15, -9, 106, -87, 963, -976, 10680, -12675, 139816, -188130, 2109915, -3149896, 36056685, -58808043, 688226911, -1212217545, 14511573174, -27357012901, 334978400547, -671079882798, ...

MCS393633 : A0 = 0; A1 = 0; A2 = 1; AK+1 = K AK-1 - AK-2 (score: 5)

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

MCS501443 (alias MCS502625) : A0 = 3; AK+1 = - AK - K + 1 (score: 5)

3, -2, 3, 0, -2, 5, -5, 3, 2, -7, 10, -8, 1, 9, -17, 18, -9, -8, 26, -35, 27, -1, -34, 61, -62, 28, 33, -95, 123, -90, -5, 128, -218, 213, -85, -133, 346, -431, 298, 48, -479, 777, -729, 250, 527, ...

MCS6489126 : A0 = 1; A1 = 1; A2 = 3; AN = - AN-1 + AN-3 (score: 5)

3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, ...

MCS125315 : A0 = 3; AN = - AN-1 + 1 (score: 4)

3, -2, 4, -1, 5, 0, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 7, 13, 8, 14, 9, 15, 10, 16, 11, 17, 12, 18, 13, 19, 14, 20, 15, 21, 16, 22, 17, 23, 18, 24, 19, 25, 20, 26, 21, 27, 22, 28, 23, 29, ...

MCS501379 : A0 = 3; AK+1 = - AK + K + 1 (score: 5)

3, -2, 5, -3, 7, -4, 9, -5, 11, -6, 13, -7, 15, -8, 17, -9, 19, -10, 21, -11, 23, -12, 25, -13, 27, -14, 29, -15, 31, -16, 33, -17, 35, -18, 37, -19, 39, -20, 41, -21, 43, -22, 45, -23, 47, -24, ...

MCS26985 : A0 = 0; A1 = 1; AK+1 = - 2 AK - AK-1 + K (score: 5)

3, -2, 5, -7, 12, -19, 31, -50, 81, -131, 212, -343, 555, -898, 1453, -2351, 3804, -6155, 9959, -16114, 26073, -42187, 68260, -110447, 178707, -289154, 467861, -757015, 1224876, -1981891, 3206767, ...

MCS864772 : A0 = 1; A1 = 3; AN = - AN-1 + AN-2 (score: 4)

Horadam sequence Wn(1, 3; 1, -1)

3, -2, 7, -23, 99, -518, 3207, -22967, 186943, -1705454, 17241483, -191361767, 2313582687, -30267936698, 426064696459, ...

MCS854404 : A0 = 1; A1 = 3; AK+1 = - K AK + AK-1 (score: 5)

3, -2, 8, -6, 19, -19, 45, -56, 110, -156, 277, -421, 711, -1118, 1844, -2946, 4807, -7735, 12561, -20276, 32858, -53112, 85993, -139081, 225099, -364154, 589280, -953406, 1542715, -2496091, ...

MCS13748 : A0 = 0; A1 = 1; AK+1 = - AK + AK-1 + K - 1 (score: 5)

3, -2, 8, -14, 46, -116, 392, -1204, 4340, -15176, 58576, -225512, 928424, -3860080, 16858016, -74759216, 344487472, -1615394144, 7816168640, -38508657376, 194832030176, ...

MCS864292 : A0 = 1; A1 = 3; AK+1 = - AK + K AK-1 (score: 5)

3, -2, 9, -12, 31, -54, 117, -224, 459, -906, 1825, -3636, 7287, -14558, 29133, -58248, 116515, -233010, 466041, -932060, 1864143, -3728262, 7456549, -14913072, 29826171, -59652314, 119304657, ...

MCS1942 (alias MCS7830, MCS13618, MCS1004960, MCS1743169)

A0 = 0; AK+1 = - 2 AK + K (score: 3)

3, -2, -2, -1, -7, -8, -8, -15, -17, -18, -26, -29, -31, -40, -44, -47, -57, -62, -66, -77, -83, -88, -100, -107, -113, -126, -134, -141, -155, -164, -172, -187, -197, -206, -222, -233, -243, ...

MCS99856 : A0 = 0; A1 = 1; A2 = 3; AK+1 = AK-2 - K (score: 5)

3, -2, -2, -4, 1, 1, 3, -2, -2, -4, 1, 1, 3, -2, -2, -4, 1, 1, 3, -2, -2, -4, 1, 1, 3, -2, -2, -4, 1, 1, 3, -2, -2, -4, 1, 1, 3, -2, -2, -4, 1, 1, 3, -2, -2, -4, 1, 1, 3, -2, -2, -4, 1, 1, 3, -2, ...

MCS6686246 : A0 = 1; A1 = 1; A2 = 3; AN = - AN-3 - 1 (score: 5)

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

MCS6297126 : A0 = 1; A1 = 1; A2 = 3; AN = - 2 AN-3 (score: 5)


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Quick Index:
    Sequences Beginning 2,0,...
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    Sequences Beginning 2,2,0,... ; 2,2,1,... ; etc.
    Sequences Beginning 2,2,4,... ; 2,2,5,... ; etc.
    Sequences Beginning 2,3,0,... ; 2,3,1,... ; etc.
    Sequences Beginning 2,3,4,... ; 2,3,5,... ; etc.
    Sequences Beginning 2,4,...
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    Sequences Beginning 3,4,... ; 3,5,... ; etc.
    Sequences Beginning 3,8,... ; 3,9,... ; etc.
    Sequences Beginning 4,0,... ; 4,1,... ; etc.
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