Minimally Complex Sequences

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2, -1, -3, 1, 8, -5, -41, 29, 286, -233, -2575, 2329, 28324, -27949, -368213, 391285, 5523194, -6260561, -93894299, 112690097, 1783991680, -2253801941, -37463825281, 49583642701, 861667981462, ...

MCS877068 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 + A_K-1 - 1 (score: 5)

2, 1, 3, 1, 9, 1, 49, 1, 385, 1, 3841, 1, 46081, 1, 645121, 1, 10321921, 1, 185794561, 1, 3715891201, 1, 81749606401, 1, ...

MCS869896 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 - K + 1 (score: 5)

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

MCS13840474 : A₀ = 2; A₁ = 1; A_N = - A_N-1 - A_N-2 (score: 5)

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

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

MCS14037082 : A₀ = 2; A₁ = 1; A_N = - A_N-2 - 1 (score: 5)

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

MCS1974 (alias MCS3926, MCS62273, MCS108608, MCS125344, MCS868869, MCS1737737, MCS3475478, MCS6950957, MCS13901914)

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

Add 2, Subtract 1

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

MCS812065 : A₀ = 0; A₁ = 1; A₂ = 1; A_N = - A_N-1 + A_N-2 + A_N-3 (score: 5)

2, -1, 3, 2, 8, 9, 17, 20, 30, 35, 47, 54, 68, 77, 93, 104, 122, 135, 155, 170, 192, 209, 233, 252, 278, 299, 327, 350, 380, 405, 437, 464, 498, 527, 563, 594, 632, 665, 705, 740, 782, 819, 863, ...

MCS501282 : A₀ = 2; A_K+1 = - A_K + K² + 1 (score: 5)

2, 1, -3, -2, 13, 11, -77, -76, 617, 685, -6169, -7534, 74029, 97943, -1036405, -1469144, 16582481, 24975449, -298484657, -474533530, 5969693141, 9965204131, -131333249101, -229199695012, ...

MCS108550 : A₀ = 0; A₁ = 2; A_K+1 = - K A_K-1 + 1 (score: 5)

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

MCS13742170 : A₀ = 2; A₁ = 1; A_K+1 = - A_K-1 - K (score: 5)

2, 1, -3, -3, 2, 6, 1, -8, -7, 7, 15, 0, -22, -15, 22, 37, -7, -59, -30, 66, 89, -36, -155, -53, 191, 208, -138, -399, -70, 537, 469, -467, -1006, -2, 1473, 1008, -1471, -2481, 463, 3952, 2018, ...

MCS6342188 : A₀ = 1; A₁ = 2; A₂ = 1; A_N = - A_N-2 - A_N-3 (score: 5)

2, 1, 3, 3, 3, 6, 4, 7, 8, 6, 12, 8, 11, 15, 8, 19, 13, 13, 25, 8, 26, 21, 10, 40, 6, 30, 37, -3, 62, 5, 23, 71, -33, 90, 16, -13, 140, -86, 112, 68, -113, 267, -156, 87, 225, -335, 469, -196, ...

MCS6504710 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - A_K + A_K-2 + K (score: 5)

2, 1, 3, 3, 4, 6, 7, 10, 13, 17, 23, 30, 40, 53, 70, 93, 123, 163, 216, 286, 379, 502, 665, 881, 1167, 1546, 2048, 2713, 3594, 4761, 6307, 8355, 11068, 14662, 19423, 25730, 34085, 45153, 59815, ...

MCS3088 (alias MCS6325292) : A₀ = 0; A₁ = 1; A₂ = 2; A_N = A_N-2 + A_N-3 (score: 4)

2, -1, 3, -3, 5, -7, 9, -15, 17, -31, 33, -63, 65, -127, 129, -255, 257, -511, 513, -1023, 1025, -2047, 2049, -4095, 4097, -8191, 8193, -16383, 16385, -32767, 32769, -65535, 65537, -131071, ...

MCS219296 : A₀ = 0; A₁ = 2; A_N = 2 A_N-2 - 1 (score: 5)

2, 1, 3, 3, 6, 7, 11, 13, 18, 21, 27, 31, 38, 43, 51, 57, 66, 73, 83, 91, 102, 111, 123, 133, 146, 157, 171, 183, 198, 211, 227, 241, 258, 273, 291, 307, 326, 343, 363, 381, 402, 421, 443, 463, ...

MCS877696 (alias MCS13705306) : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 + K - 1 (score: 4)

2, -1, -3, 3, 7, -5, -13, 11, 27, -21, -53, 43, 107, -85, -213, 171, 427, -341, -853, 683, 1707, -1365, -3413, 2731, 6827, -5461, -13653, 10923, 27307, -21845, -54613, 43691, 109227, -87381, ...

MCS869056 : A₀ = 1; A₁ = 2; A_N = - 2 A_N-2 + 1 (score: 4)

2, 1, 3, 3, 10, 13, 51, 79, 358, 633, 3223, 6331, 35454, 75973, 460903, 1063623, 6913546, 17017969, 117530283, 306323443, 2233075378, 6126468861, 46894582939, 134782314943, ...

MCS869128 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 - A_K-1 + 1 (score: 5)

2, -1, 3, 4, 1, 5, 6, 3, 7, 8, 5, 9, 10, 7, 11, 12, 9, 13, 14, 11, 15, 16, 13, 17, 18, 15, 19, 20, 17, 21, 22, 19, 23, 24, 21, 25, 26, 23, 27, 28, 25, 29, 30, 27, 31, 32, 29, 33, 34, 31, 35, 36, ...

MCS1731264 : A₀ = 1; A₁ = 2; A_K+1 = - A_K - A_K-1 + 2 K (score: 5)

2, 1, 3, 4, 3, 7, 5, 7, 10, 6, 13, 10, 10, 18, 8, 19, 17, 10, 29, 9, 23, 29, 4, 44, 11, 20, 52, -12, 62, 21, -1, 96, -41, 75, 57, -61, 174, -78, 57, 158, -194, 294, -92, -57, 397, -442, 433, 13, ...

MCS6504717 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = - A_K + A_K-2 + K (score: 5)

2, -1, -3, 4, 5, -11, -6, 27, 1, -60, 25, 121, -110, -217, 341, 324, -899, -307, 2122, -285, -4551, 2692, 8817, -9935, -14942, 28687, 19949, -72316, -11211, 164581, -49894, -340373, 264369, ...

MCS6336774 : A₀ = 1; A₁ = 1; A₂ = 2; A_N = - 2 A_N-2 + A_N-3 (score: 5)

2, -1, 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, ...

MCS216192 : A₀ = 1; A₁ = 2; A_N = - A_N-1 + A_N-2 (score: 3)

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

2, 1, 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, ...

MCS13770842 : A₀ = 2; A₁ = 1; A_N = A_N-1 + A_N-2 (score: 5)

Lucas numbers starting with 2 (A0032)

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

2, -1, 3, -4, 11, -21, 65, -148, 519, -1333, 5189, -14664, 62267, -190633, 871737, -2859496, 13947791, -48611433, 251060237, -923617228, 5021204739, -19395961789, 110466504257, -446107121148, ...

MCS109572 : A₀ = 0; A₁ = 2; A_K+1 = K A_K-1 - 1 (score: 5)

2, -1, -3, -5, 1, 5, 9, -3, -11, -19, 5, 21, 37, -11, -43, -75, 21, 85, 149, -43, -171, -299, 85, 341, 597, -171, -683, -1195, 341, 1365, 2389, -683, -2731, -4779, 1365, 5461, 9557, -2731, -10923, ...

MCS26117 : A₀ = 0; A₁ = 1; A₂ = 2; A_N = - 2 A_N-3 - 1 (score: 5)

2, 1, -3, -5, 1, 11, 9, -13, -31, -5, 57, 67, -47, -181, -87, 275, 449, -101, -999, -797, 1201, 2795, 393, -5197, -5983, 4411, 16377, 7555, -25199, -40309, 10089, 90707, 70529, -110885, -251943, ...

MCS55095386 : A₀ = 2; A₁ = 1; A_N = A_N-1 - 2 A_N-2 (score: 6)

An unusually oscillating sequence (A2249)

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

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

MCS25697 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = - A_K-2 - K + 1 (score: 5)

2, 1, 3, 5, 3, 7, 11, 7, 15, 23, 15, 31, 47, 31, 63, 95, 63, 127, 191, 127, 255, 383, 255, 511, 767, 511, 1023, 1535, 1023, 2047, 3071, 2047, 4095, 6143, 4095, 8191, 12287, 8191, 16383, 24575, ...

MCS12802 : A₀ = 0; A₁ = 1; A₂ = 2; A_N = 2 A_N-3 + 1 (score: 5)

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

MCS6391340 : A₀ = 1; A₁ = 2; A₂ = 1; A_K+1 = - A_K-2 - K (score: 5)

2, 1, 3, 5, 5, 8, 11, 12, 16, 20, 22, 27, 32, 35, 41, 47, 51, 58, 65, 70, 78, 86, 92, 101, 110, 117, 127, 137, 145, 156, 167, 176, 188, 200, 210, 223, 236, 247, 261, 275, 287, 302, 317, 330, 346, ...

MCS13088 (alias MCS6358060) : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = A_K-2 + K - 1 (score: 5)

2, -1, -3, -5, -12, -43, -203, -1175, -8022, -63001, -558987, -5526869, -60236572, -717311995, -9264819363, -128990159087, ...

MCS865088 : A₀ = 1; A₁ = 2; A_K+1 = K A_K - A_K - A_K-1 (score: 5)

2, -1, -3, 5, 15, -21, -85, 153, 687, -1369, -6861, 15069, 82343, -195885, -1152789, 2938289, 18444639, -49950897, -332003485, 949067061, 6640069719, -19930408261, -146081533797, 458399390025, ...

MCS877580 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 + K - 1 (score: 5)

2, 1, -3, -6, 6, 36, 0, -252, -252, 2016, 4536, -17640, -72072, 157248, 1166256, -1192464, -19852560, 419328, 357765408, 349798176, -6805509984, -14151271680, 135569947968, 461049196608, ...

MCS215052 : A₀ = 1; A₁ = 2; A_K+1 = A_K - K A_K-1 (score: 4)

2, 1, -3, -7, -8, -6, -4, -5, -9, -13, -14, -12, -10, -11, -15, -19, -20, -18, -16, -17, -21, -25, -26, -24, -22, -23, -27, -31, -32, -30, -28, -29, -33, -37, -38, -36, -34, -35, -39, -43, -44, ...

MCS430944 : A₀ = 0; A₁ = 2; A_K+1 = A_K - A_K-1 - K (score: 5)

2, 1, 3, 7, 24, 103, 539, 3337, 23898, 194521, 1774587, 17940391, 199118888, 2407367047, 31494890499, 443335834033, ...

MCS864832 : A₀ = 1; A₁ = 2; A_K+1 = K A_K - A_K + A_K-1 (score: 5)

2, -1, 3, -8, 10, -31, 45, -114, 196, -433, 815, -1692, 3310, -6707, 13313, -26742, 53352, -106853, 213539, -427264, 854322, -1708871, 3417493, -6835258, 13670220, -27340761, 54681175, -109362724, ...

MCS1731904 : A₀ = 1; A₁ = 2; A_K+1 = - A_K + 2 A_K-1 - K (score: 5)

2, -1, 3, -8, 33, -164, 985, -6894, 55153, -496376, 4963761, -54601370, 655216441, -8517813732, 119249392249, ...

MCS501346 : A₀ = 2; A_K+1 = - K A_K - A_K + 1 (score: 5)

2, 1, 3, 9, 14, 17, 23, 33, 42, 49, 59, 73, 86, 97, 111, 129, 146, 161, 179, 201, 222, 241, 263, 289, 314, 337, 363, 393, 422, 449, 479, 513, 546, 577, 611, 649, 686, 721, 759, 801, 842, 881, 923, ...

MCS869152 : A₀ = 1; A₁ = 2; A_K+1 = - A_K-1 + K² + 1 (score: 5)

2, -1, -3, -9, -31, -129, -651, -3913, -27399, -219201, -1972819, -19728201, -217010223, -2604122689, -33853594971, -473950329609, ...

MCS504642 : A₀ = 2; A_K+1 = K A_K - K - 1 (score: 5)

2, 1, 3, 9, 31, 129, 651, 3913, 27399, 219201, 1972819, 19728201, 217010223, 2604122689, 33853594971, 473950329609, ...

MCS500290 : A₀ = 2; A_K+1 = K A_K + K + 1 (score: 5)

2, -1, -3, -11, -20, -37, -57, -87, -122, -169, -223, -291, -368, -461, -565, -687, -822, -977, -1147, -1339, -1548, -1781, -2033, -2311, -2610, -2937, -3287, -3667, -4072, -4509, -4973, -5471, ...

MCS877104 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 - K² - 1 (score: 5)

2, -1, -3, -13, -79, -633, -6331, -75973, -1063623, -17017969, -306323443, -6126468861, -134782314943, ...

MCS252066 : A₀ = 2; A_K+1 = 2 K A_K - 1 (score: 5)

2, 1, 3, 13, 79, 633, 6331, 75973, 1063623, 17017969, 306323443, 6126468861, 134782314943, ...

MCS250018 : A₀ = 2; A_K+1 = 2 K A_K + 1 (score: 5)

2, 1, 4, 0, 6, -2, 11, -7, 20, -19, 39, -45, 79, -102, 164, -225, 346, -490, 736, -1060, 1573, -2285, 3370, -4917, 7229, -10571, 15517, -22716, 33318, -48803, 71552, -104836, 153674, -225190, ...

MCS26019382 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = - A_K - A_K-2 + K (score: 5)

2, -1, 4, 1, 6, 3, 8, 5, 10, 7, 12, 9, 14, 11, 16, 13, 18, 15, 20, 17, 22, 19, 24, 21, 26, 23, 28, 25, 30, 27, 32, 29, 34, 31, 36, 33, 38, 35, 40, 37, 42, 39, 44, 41, 46, 43, 48, 45, 50, 47, 52, ...

MCS1002818 : A₀ = 2; A_K+1 = - A_K + 2 K + 1 (score: 5)

2, 1, 4, 1, 8, -1, 16, -9, 34, -33, 78, -99, 190, -275, 480, -739, 1236, -1957, 3212, -5149, 8382, -13509, 21914, -35399, 57338, -92711, 150076, -242759, 392864, -635593, 1028488, -1664049, ...

MCS3486848 : A₀ = 1; A₁ = 2; A_K+1 = - A_K + A_K-1 + K + 1 (score: 5)

2, -1, -4, -1, 8, -1, -46, -1, 314, -1, -2836, -1, 31184, -1, -405406, -1, 6081074, -1, -103378276, -1, 1964187224, -1, -41247931726, -1, 948702429674, -1, ...

MCS858636 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 + A_K-1 - K (score: 5)

2, 1, 4, -1, 10, -11, 32, -53, 118, -223, 460, -905, 1826, -3635, 7288, -14557, 29134, -58247, 116516, -233009, 466042, -932059, 1864144, -3728261, 7456550, -14913071, 29826172, -59652313, ...

MCS1743168 (alias MCS6972678) : A₀ = 1; A₁ = 2; A_N = - A_N-1 + 2 A_N-2 + 1 (score: 5)

2, 1, 4, 1, 16, 1, 106, 1, 946, 1, 10396, 1, 135136, 1, 2027026, 1, 34459426, 1, 654729076, 1, 13749310576, 1, 316234143226, 1, ...

MCS858632 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 + A_K-1 - K (score: 5)

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

MCS107360 : A₀ = 0; A₁ = 2; A_K+1 = - A_K-1 - K (score: 4)

2, 1, -4, -2, 8, 4, -16, -8, 32, 16, -64, -32, 128, 64, -256, -128, 512, 256, -1024, -512, 2048, 1024, -4096, -2048, 8192, 4096, -16384, -8192, 32768, 16384, -65536, -32768, 131072, 65536, ...

MCS13676634 : A₀ = 2; A₁ = 1; A_N = - 2 A_N-2 (score: 5)

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

2, 1, 4, 2, 8, 4, 16, 8, 32, 16, 64, 32, 128, 64, 256, 128, 512, 256, 1024, 512, 2048, 1024, 4096, 2048, 8192, 4096, 16384, 8192, 32768, 16384, 65536, 32768, 131072, 65536, 262144, 131072, 524288, ...

MCS6836314 : A₀ = 2; A₁ = 1; A_N = 2 A_N-2 (score: 5)

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

2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 52, ...

MCS7898 (alias MCS501409, MCS1745413) : A₀ = 0; A_K+1 = - A_K + 2 K - 1 (score: 4)

2, -1, 4, -3, 6, -5, 8, -7, 10, -9, 12, -11, 14, -13, 16, -15, 18, -17, 20, -19, 22, -21, 24, -23, 26, -25, 28, -27, 30, -29, 32, -31, 34, -33, 36, -35, 38, -37, 40, -39, 42, -41, 44, -43, 46, ...

MCS12688 : A₀ = 0; A₁ = 1; A₂ = 2; A_N = - A_N-1 + A_N-2 + A_N-3 (score: 5)

2, 1, -4, 3, 6, -11, 0, 23, -22, -23, 68, -21, -114, 157, 72, -385, 242, 529, -1012, -45, 2070, -1979, -2160, 6119, -1798, -10439, 14036, 6843, -34914, 21229, 48600, -91057, -6142, 188257, ...

MCS27237 (alias MCS792737, MCS3486401) : A₀ = 0; A₁ = 1; A_N = - A_N-1 - 2 A_N-2 + 1 (score: 5)

2, -1, -4, -3, 6, 11, 0, -23, -22, 23, 68, 21, -114, -157, 72, 385, 242, -529, -1012, 45, 2070, 1979, -2160, -6119, -1798, 10439, 14036, -6843, -34914, -21229, 48600, 91057, -6142, -188257, ...

MCS24773 : A₀ = 0; A₁ = 1; A₂ = 2; A_N = - A_N-2 - 2 A_N-3 (score: 5)

2, -1, 4, -3, 10, -9, 24, -27, 58, -77, 144, -211, 366, -565, 944, -1495, 2454, -3933, 6404, -10319, 16742, -27041, 43804, -70823, 114650, -185449, 300124, -485547, 785698, -1271217, 2056944, ...

MCS3519616 : A₀ = 1; A₁ = 2; A_K+1 = - A_K + A_K-1 + K - 1 (score: 5)

2, -1, -4, 3, 16, -15, -96, 105, 768, -945, -7680, 10395, 92160, -135135, -1290240, 2027025, 20643840, -34459425, -371589120, 654729075, 7431782400, -13749310575, -163499212800, 316234143225, ...

MCS53260 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 (score: 3)

2, 1, 4, 3, 16, 15, 96, 105, 768, 945, 7680, 10395, 92160, 135135, 1290240, 2027025, 20643840, 34459425, 371589120, 654729075, 7431782400, 13749310575, 163499212800, 316234143225, ...

MCS53256 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 (score: 3)

Interleaves (2N-1)!! (A1147) with 2*(2N!!) (A66318)

2, 1, 4, 4, 8, 9, 14, 16, 22, 25, 32, 36, 44, 49, 58, 64, 74, 81, 92, 100, 112, 121, 134, 144, 158, 169, 184, 196, 212, 225, 242, 256, 274, 289, 308, 324, 344, 361, 382, 400, 422, 441, 464, 484, ...

MCS107072 : A₀ = 0; A₁ = 2; A_K+1 = A_K-1 + K (score: 4)

2, -1, 4, -4, 9, -12, 22, -33, 56, -88, 145, -232, 378, -609, 988, -1596, 2585, -4180, 6766, -10945, 17712, -28656, 46369, -75024, 121394, -196417, 317812, -514228, 832041, -1346268, 2178310, ...

MCS3404 (alias MCS435776, MCS791649, MCS871553, MCS1743105, MCS13944854)

A₀ = 0; A₁ = 1; A_N = - A_N-1 + A_N-2 + 1 (score: 4)

2, 1, 4, 4, 9, 12, 22, 33, 56, 88, 145, 232, 378, 609, 988, 1596, 2585, 4180, 6766, 10945, 17712, 28656, 46369, 75024, 121394, 196417, 317812, 514228, 832041, 1346268, 2178310, 3524577, 5702888, ...

MCS791617 : A₀ = 0; A₁ = 0; A₂ = 1; A_N = 2 A_N-2 + A_N-3 (score: 5)

2, 1, 4, 5, 6, 13, 16, 25, 42, 57, 92, 141, 206, 325, 488, 737, 1138, 1713, 2612, 3989, 6038, 9213, 14016, 21289, 32442, 49321, 75020, 114205, 173662, 264245, 402072, 611569, 930562, 1415713, ...

MCS12354 (alias MCS790689) : A₀ = 0; A₁ = 1; A₂ = 2; A_N = A_N-2 + 2 A_N-3 (score: 5)

2, -1, -4, -5, -8, -15, -22, -27, -34, -45, -56, -65, -76, -91, -106, -119, -134, -153, -172, -189, -208, -231, -254, -275, -298, -325, -352, -377, -404, -435, -466, -495, -526, -561, -596, -629, ...

MCS856880 : A₀ = 1; A₁ = 2; A_K+1 = - A_K-1 - K² + K (score: 5)

2, 1, 4, 5, 16, 25, 86, 157, 610, 1265, 5500, 12661, 60512, 151945, 786670, 2127245, 11800066, 34035937, 200601140, 612646885, 3811421680, 12252937721, 80039855302, 269564629885, ...

MCS856840 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 - A_K-1 + K (score: 5)

2, -1, -4, -7, -10, -13, -16, -19, -22, -25, -28, -31, -34, -37, -40, -43, -46, -49, -52, -55, -58, -61, -64, -67, -70, -73, -76, -79, -82, -85, -88, -91, -94, -97, -100, -103, -106, -109, -112, ...

MCS28335 (alias MCS1015042) : A_K = - 3 K + 2 (score: 5)

2, -1, 4, -7, 14, -29, 56, -115, 226, -457, 908, -1823, 3638, -7285, 14560, -29131, 58250, -116513, 233012, -466039, 932062, -1864141, 3728264, -7456547, 14913074, -29826169, 59652316, -119304655, ...

MCS1759552 : A₀ = 1; A₁ = 2; A_N = - A_N-1 + 2 A_N-2 - 1 (score: 5)

2, 1, -4, -7, 14, 57, -40, -495, -134, 4817, 6292, -51511, -133306, 587849, 2587440, -6818143, -50804622, 71921953, 1037209772, -401229287, -22182634498, -13355590183, 496845003272, 817379167665, ...

MCS108801 : A₀ = 0; A₁ = 1; A_K+1 = A_K - K A_K-1 + 1 (score: 5)

2, 1, 4, 7, 16, 27, 46, 69, 102, 141, 192, 251, 324, 407, 506, 617, 746, 889, 1052, 1231, 1432, 1651, 1894, 2157, 2446, 2757, 3096, 3459, 3852, 4271, 4722, 5201, 5714, 6257, 6836, 7447, 8096, ...

MCS858656 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 + K² - K (score: 5)

2, -1, -4, 7, 24, -37, -162, 303, 1466, -3021, -16116, 36263, 209520, -507669, -3142786, 8122719, 53427378, -146208925, -1015120164, 2924178519, 21317523464, -64331927397, -490303039650, ...

MCS856844 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 - A_K-1 + K (score: 5)

2, 1, 4, -7, 46, -263, 1856, -14831, 133498, -1334959, 14684572, -176214839, 2290792934, -32071101047, 481066515736, ...

MCS15637 (alias MCS250200) : A₀ = 0; A_K+1 = - K A_K + 2 K + 1 (score: 5)

2, 1, -4, -11, -10, 13, 56, 73, -22, -263, -460, -131, 1118, 2629, 1904, -4079, -13870, -15503, 10604, 67717, 103622, 4093, -302680, -617639, -327238, 1198441, 3378596, 3161869, -3812050, ...

MCS26959 : A₀ = 0; A₁ = 1; A_N = 2 A_N-1 - 3 A_N-2 (score: 6)

An unusually oscillating sequence (A88137)

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

2, 1, 4, 11, 16, 19, 26, 37, 46, 53, 64, 79, 92, 103, 118, 137, 154, 169, 188, 211, 232, 251, 274, 301, 326, 349, 376, 407, 436, 463, 494, 529, 562, 593, 628, 667, 704, 739, 778, 821, 862, 901, ...

MCS856864 : A₀ = 1; A₁ = 2; A_K+1 = - A_K-1 + K² + K (score: 5)

2, -1, -4, -13, -24, -43, -66, -99, -138, -189, -248, -321, -404, -503, -614, -743, -886, -1049, -1228, -1429, -1648, -1891, -2154, -2443, -2754, -3093, -3456, -3849, -4268, -4719, -5198, -5711, ...

MCS858672 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 - K² - K (score: 5)

2, -1, 4, -13, 56, -293, 1814, -12991, 105742, -964669, 9752432, -108241421, 1308649484, -17120684713, 240998235466, ...

MCS213600 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K + A_K-1 (score: 4)

2, 1, -4, -15, -34, -63, -104, -159, -230, -319, -428, -559, -714, -895, -1104, -1343, -1614, -1919, -2260, -2639, -3058, -3519, -4024, -4575, -5174, -5823, -6524, -7279, -8090, -8959, -9888, ...

MCS62609 (alias MCS500940) : A₀ = 0; A_K+1 = A_K - K² + K + 1 (score: 5)

2, 1, -4, -17, -46, -107, -232, -485, -994, -2015, -4060, -8153, -16342, -32723, -65488, -131021, -262090, -524231, -1048516, -2097089, -4194238, -8388539, -16777144, -33554357, -67108786, ...

MCS497136 : A₀ = 1; A_K+1 = 2 A_K - 3 K (score: 5)

2, -1, 4, -19, 134, -1205, 13256, -172327, 2584906, -43943401, 834924620, -17533417019, 403268591438, ...

MCS500824 : A₀ = 1; A_K+1 = - 2 K A_K + A_K + 1 (score: 5)

2, 1, 5, 0, 14, -9, 43, -54, 148, -247, 553, -1036, 2154, -4213, 8535, -16946, 34032, -67907, 135989, -271784, 543782, -1087329, 2174915, -4349550, 8699404, -17398479, 34797313, -69594244, ...

MCS1730880 : A₀ = 1; A₁ = 2; A_K+1 = - A_K + 2 A_K-1 + K (score: 5)

2, -1, -5, 1, 9, -3, -19, 5, 37, -11, -75, 21, 149, -43, -299, 85, 597, -171, -1195, 341, 2389, -683, -4779, 1365, 9557, -2731, -19115, 5461, 38229, -10923, -76459, 21845, 152917, -43691, -305835, ...

MCS438624 : A₀ = 0; A₁ = 2; A_N = - 2 A_N-2 - 1 (score: 5)

2, 1, 5, 1, 10, -2, 20, -13, 43, -45, 100, -132, 246, -363, 625, -971, 1614, -2566, 4200, -6745, 10967, -17689, 28680, -46344, 75050, -121367, 196445, -317783, 514258, -832010, 1346300, -2178277, ...

MCS1730817 (alias MCS3486849) : A₀ = -1; A₁ = 0; A_K+1 = - A_K + A_K-1 + K (score: 5)

2, -1, -5, 1, 17, -9, -107, 57, 849, -521, -8499, 5721, 101977, -74385, -1427691, 1115761, 22843041, -18967953, -411174755, 360391089, 8223495081, -7568212889, -180916891803, 174068896425, ...

MCS869900 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 - K + 1 (score: 5)

2, 1, 5, 2, 11, 1, 22, -7, 45, -34, 99, -111, 234, -319, 581, -870, 1483, -2319, 3838, -6119, 9997, -16074, 26115, -42143, 68306, -110399, 178757, -289102, 467915, -756959, 1224934, -1981831, ...

MCS1731200 : A₀ = 1; A₁ = 2; A_K+1 = - A_K + A_K-1 + 2 K (score: 5)

2, 1, 5, -2, 17, -23, 74, -143, 365, -794, 1889, -4271, 9938, -22751, 52565, -120818, 278513, -640967, 1476506, -3399407, 7828925, -18027146, 41513921, -95595359, 220137122, -506923199, ...

MCS432576 (alias MCS1730310) : A₀ = 1; A₁ = 2; A_N = - A_N-1 + 3 A_N-2 (score: 5)

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

2, -1, -5, 2, 19, -11, -115, 76, 919, -685, -9191, 7534, 110291, -97943, -1544075, 1469144, 24705199, -24975449, -444693583, 474533530, 8893871659, -9965204131, -195665176499, 229199695012, ...

MCS109574 : A₀ = 0; A₁ = 2; A_K+1 = - K A_K-1 - 1 (score: 5)

2, 1, 5, 2, 24, 7, 166, 32, 1487, 154, 16325, 361, 212071, -11271, 3180704, -392407, 54083239, -10244030, 1027973948, -258963839, 21597696938, -6725178406, 497005993413, -183001978682, ...

MCS1574534 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = K A_K-1 - A_K-2 (score: 5)

2, 1, 5, 3, 11, 7, 23, 15, 47, 31, 95, 63, 191, 127, 383, 255, 767, 511, 1535, 1023, 3071, 2047, 6143, 4095, 12287, 8191, 24575, 16383, 49151, 32767, 98303, 65535, 196607, 131071, 393215, 262143, ...

MCS217248 : A₀ = 0; A₁ = 2; A_N = 2 A_N-2 + 1 (score: 5)

2, -1, 5, -3, 12, -10, 28, -31, 67, -89, 166, -244, 422, -653, 1089, -1727, 2832, -4542, 7392, -11915, 19327, -31221, 50570, -81768, 132362, -214105, 346493, -560571, 907092, -1467634, 2374756, ...

MCS432704 : A₀ = 0; A₁ = 2; A_K+1 = - A_K + A_K-1 + K (score: 5)

2, 1, 5, 3, 24, 17, 167, 135, 1502, 1349, 16521, 16187, 214772, 226617, 3221579, 3625871, 54766842, 65265677, 1040569997, 1305313539, 21851969936, 28716897857, 502595308527, 689205548567, ...

MCS877064 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 + A_K-1 - 1 (score: 5)

2, 1, -5, -3, 26, 19, -181, -151, 1630, 1511, -17929, -18131, 233078, 253835, -3496169, -4061359, 59434874, 73104463, -1129262605, -1462089259, 23714514706, 32165963699, -545433838237, ...

MCS434201 : A₀ = -1; A₁ = 0; A_K+1 = - K A_K-1 + 1 (score: 5)

2, 1, 5, 4, 21, 21, 127, 148, 1017, 1333, 10171, 14664, 122053, 190633, 1708743, 2859496, 27339889, 48611433, 492118003, 923617228, 9842360061, 19395961789, 216531921343, 446107121148, ...

MCS108548 : A₀ = 0; A₁ = 2; A_K+1 = K A_K-1 + 1 (score: 5)

2, 1, 5, 5, 23, 29, 143, 209, 1151, 1889, 11519, 20789, 138239, 270269, 1935359, 4054049, 30965759, 68918849, 557383679, 1309458149, 11147673599, 27498621149, 245248819199, 632468286449, ...

MCS877576 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 + K - 1 (score: 5)

2, -1, -5, 5, 26, -29, -181, 233, 1630, -2329, -17929, 27949, 233078, -391285, -3496169, 6260561, 59434874, -112690097, -1129262605, 2253801941, 23714514706, -49583642701, -545433838237, ...

MCS869132 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 - A_K-1 + 1 (score: 5)

2, 1, -5, 6, 0, -11, 17, -6, -22, 45, -29, -38, 112, -103, -47, 262, -318, 9, 571, -898, 336, 1133, -2367, 1570, 1930, -5867, 5507, 2290, -13664, 16881, -927, -29618, 47426, -18735, -58309, ...

MCS812577 : A₀ = 0; A₁ = 1; A₂ = 1; A_N = - A_N-1 - A_N-2 + A_N-3 (score: 5)

2, -1, -5, -6, -3, 1, 2, -1, -5, -6, -3, 1, 2, -1, -5, -6, -3, 1, 2, -1, -5, -6, -3, 1, 2, -1, -5, -6, -3, 1, 2, -1, -5, -6, -3, 1, 2, -1, -5, -6, -3, 1, 2, -1, -5, -6, -3, 1, 2, -1, -5, -6, -3, ...

MCS3500224 : A₀ = 1; A₁ = 2; A_N = A_N-1 - A_N-2 - 2 (score: 5)

2, 1, 5, 6, 12, 15, 23, 28, 38, 45, 57, 66, 80, 91, 107, 120, 138, 153, 173, 190, 212, 231, 255, 276, 302, 325, 353, 378, 408, 435, 467, 496, 530, 561, 597, 630, 668, 703, 743, 780, 822, 861, 905, ...

MCS15704 : A₀ = 0; A_K+1 = - A_K + K² + 2 (score: 5)

2, -1, -5, 6, 24, -41, -162, 352, 1417, -3682, -15235, 45601, 194373, -653649, -2869994, 10652757, 48136249, -194619620, -903935974, 3940528649, 18788035834, -87595566252, -428184295533, ...

MCS1574086 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - K A_K-1 + A_K-2 (score: 5)

2, -1, -5, -7, -10, -17, -25, -31, -38, -49, -61, -71, -82, -97, -113, -127, -142, -161, -181, -199, -218, -241, -265, -287, -310, -337, -365, -391, -418, -449, -481, -511, -542, -577, -613, -647, ...

MCS869168 : A₀ = 1; A₁ = 2; A_K+1 = - A_K-1 - K² + 1 (score: 5)

2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, 2047, 4097, 8191, 16385, 32767, 65537, 131071, 262145, 524287, 1048577, 2097151, 4194305, 8388607, 16777217, 33554431, 67108865, 134217727, 268435457, ...

MCS27545690 : A₀ = 2; A₁ = 1; A_N = A_N-1 + 2 A_N-2 (score: 6)

Jacobsthal-Lucas numbers (A14551)

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

2, 1, -5, -8, 7, 31, 10, -83, -113, 136, 475, 67, -1358, -1559, 2515, 7192, -353, -21929, -20870, 44917, 107527, -27224, -349805, -268133, 781282, 1585681, -758165, -5515208, -3240713, 13304911, ...

MCS110227546 : A₀ = 2; A₁ = 1; A_N = A_N-1 - 3 A_N-2 (score: 7)

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

2, -1, 5, -8, 28, -68, 236, -712, 2600, -9008, 35008, -134096, 554192, -2297440, 10056128, -44517728, 205415776, -962217152, 4659701120, -22941827008, 116135849408, -597914216576, ...

MCS216072 : A₀ = 1; A₁ = 2; A_K+1 = - A_K + K A_K-1 (score: 4)

2, 1, 5, 9, 20, 33, 55, 81, 118, 161, 217, 281, 360, 449, 555, 673, 810, 961, 1133, 1321, 1532, 1761, 2015, 2289, 2590, 2913, 3265, 3641, 4048, 4481, 4947, 5441, 5970, 6529, 7125, 7753, 8420, ...

MCS877088 : A₀ = 1; A₁ = 2; A_K+1 = A_K-1 + K² - 1 (score: 5)

2, -1, -5, -11, -15, -16, -12, -5, 2, 4, -2, -16, -33, -45, -44, -27, 1, 27, 35, 14, -34, -91, -128, -118, -52, 50, 141, 165, 86, -85, -281, -399, -347, -100, 264, 575, 638, 336, -278, -956, ...

MCS6447494 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K - A_K-2 - K (score: 5)

2, -1, -6, 0, 20, -5, -126, 28, 1000, -261, -10010, 2860, 120108, -37193, -1681526, 557880, 26904400, -9483977, -484279218, 180195544, 9685584340, -3784106445, -213082855502, 87034448212, ...

MCS107270 : A₀ = 0; A₁ = 2; A_K+1 = - K A_K-1 - K (score: 5)

2, -1, -6, -1, 8, -3, -22, -1, 36, -7, -82, 3, 152, -19, -318, 23, 620, -63, -1258, 107, 2496, -235, -5014, 447, 10004, -919, -20034, 1811, 40040, -3651, -80110, 7271, 160188, -14575, -320410, ...

MCS429408 : A₀ = 0; A₁ = 2; A_K+1 = - 2 A_K-1 - K (score: 5)

2, -1, 6, -3, 14, -11, 32, -35, 76, -101, 188, -277, 478, -741, 1234, -1959, 3210, -5151, 8380, -13511, 21912, -35401, 57336, -92713, 150074, -242761, 392862, -635595, 1028486, -1664051, 2692568, ...

MCS3461637 : A₀ = 0; A₁ = -1; A_K+1 = - A_K + A_K-1 + K (score: 5)

2, 1, 6, 3, 44, 25, 522, 343, 8344, 6165, 166870, 135619, 4004868, 3526081, 112136290, 105782415, 3588361264, 3596602093, 129181005486, 136670879515, ...

MCS429076 : A₀ = 1; A₁ = 2; A_K+1 = 2 K A_K-1 - K (score: 5)

2, -1, -6, -5, 6, 15, 2, -29, -34, 23, 90, 43, -138, -225, 50, 499, 398, -601, -1398, -197, 2598, 2991, -2206, -8189, -3778, 12599, 20154, -5045, -45354, -35265, 55442, 125971, 15086, -236857, ...

MCS3515072 : A₀ = 1; A₁ = 2; A_N = A_N-1 - 2 A_N-2 - 1 (score: 5)

2, 1, 6, 5, 16, 15, 38, 37, 84, 83, 178, 177, 368, 367, 750, 749, 1516, 1515, 3050, 3049, 6120, 6119, 12262, 12261, 24548, 24547, 49122, 49121, 98272, 98271, 196574, 196573, 393180, 393179, ...

MCS214176 : A₀ = 0; A₁ = 2; A_K+1 = 2 A_K-1 + K (score: 5)

2, -1, -6, 5, 42, -45, -462, 585, 6930, -9945, -131670, 208845, 3028410, -5221125, -81767070, 151412625, 2534779170, -4996616625, -88717270950, 184874815125, ...

MCS854060 : A₀ = 1; A₁ = 2; A_K+1 = - 2 K A_K-1 + A_K-1 (score: 5)

2, 1, 6, 5, 42, 45, 462, 585, 6930, 9945, 131670, 208845, 3028410, 5221125, 81767070, 151412625, 2534779170, 4996616625, 88717270950, 184874815125, ...

MCS427540 : A₀ = 1; A₁ = 2; A_K+1 = 2 K A_K-1 - A_K-1 (score: 5)

2, 1, 6, 6, 28, 35, 174, 252, 1400, 2277, 14010, 25058, 168132, 325767, 2353862, 4886520, 37661808, 83070857, 677912562, 1578346302, 13558251260, 33145272363, 298281527742, 762341264372, ...

MCS107012 : A₀ = 0; A₁ = 2; A_K+1 = K A_K-1 + K (score: 5)

2, -1, 6, -7, 20, -33, 74, -139, 288, -565, 1142, -2271, 4556, -9097, 18210, -36403, 72824, -145629, 291278, -582535, 1165092, -2330161, 4660346, -9320667, 18641360, -37282693, 74565414, ...

MCS15702 : A₀ = 0; A_K+1 = - 2 A_K + K + 2 (score: 5)

2, -1, -6, -8, -10, -17, -26, -32, -38, -49, -62, -72, -82, -97, -114, -128, -142, -161, -182, -200, -218, -241, -266, -288, -310, -337, -366, -392, -418, -449, -482, -512, -542, -577, -614, -648, ...

MCS106904 : A₀ = 0; A₁ = 2; A_K+1 = - A_K-1 - K² (score: 5)

2, -1, -6, -9, -8, -5, -4, -7, -12, -15, -14, -11, -10, -13, -18, -21, -20, -17, -16, -19, -24, -27, -26, -23, -22, -25, -30, -33, -32, -29, -28, -31, -36, -39, -38, -35, -34, -37, -42, -45, -44, ...

MCS3516096 : A₀ = 1; A₁ = 2; A_K+1 = A_K - A_K-1 - K - 1 (score: 5)

2, -1, -6, 9, 52, -85, -618, 1197, 9896, -21537, -197910, 473825, 4749852, -12319437, -132995842, 369583125, 4255866960, -12565826233, -153211210542, 477501396873, ...

MCS856108 : A₀ = 1; A₁ = 2; A_K+1 = - 2 K A_K-1 + K (score: 5)

2, 1, 6, 10, 22, 35, 58, 84, 122, 165, 222, 286, 366, 455, 562, 680, 818, 969, 1142, 1330, 1542, 1771, 2026, 2300, 2602, 2925, 3278, 3654, 4062, 4495, 4962, 5456, 5986, 6545, 7142, 7770, 8438, ...

MCS106768 : A₀ = 0; A₁ = 2; A_K+1 = A_K-1 + K² (score: 5)

2, -1, -6, 11, 48, -81, -424, 819, 4674, -9817, -60750, 137451, 911264, -2199201, -15491472, 39585635, 294337986, -791712681, -6181097686, 17417679003, 142165246800, -418024296049, ...

MCS877581 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K-1 + K - 1 (score: 5)

2, -1, -6, 11, 48, -81, -424, 819, 4674, -9817, -60750, 137451, 911264, -2199201, -15491472, 39585635, 294337986, -791712681, -6181097686, 17417679003, 142165246800, -418024296049, ...

MCS856845 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K-1 - A_K-1 + K (score: 5)

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