Minimally Complex Sequences

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

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

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

MCS855090 : A₀ = 2; A₁ = 3; A_K+1 = - K A_K-1 - A_K-1 (score: 5)

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

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

2, -3, 4, -9, 32, -151, 874, -5967, 46862, -415791, 4111048, -44805737, 533557796, -6891445611, 95946680758, ...

MCS213856 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K - A_K-1 (score: 4)

2, 3, -4, -10, 30, 77, -232, -684, 2330, 7535, -27948, -97942, 391286, 1469145, -6260560, -24975448, 112690098, 474533531, -2253801940, -9965204130, 49583642702, 229199695013, ...

MCS3424470 : A₀ = 1; A₁ = 0; A_K+1 = - K A_K-1 + K (score: 5)

2, 3, -4, 11, -26, 63, -152, 367, -886, 2139, -5164, 12467, -30098, 72663, -175424, 423511, -1022446, 2468403, -5959252, 14386907, -34733066, 83853039, -202439144, 488731327, -1179901798, ...

MCS3453442 : A₀ = 2; A₁ = 3; A_N = - 2 A_N-1 + A_N-2 (score: 5)

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

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

MCS852146 : A₀ = 2; A₁ = 3; A_K+1 = - 2 K A_K-1 (score: 5)

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

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

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

MCS878272 : A₀ = 1; A₁ = 2; A_K+1 = - A_K-1 - K - 1 (score: 4)

2, 3, -5, 1, -7, 17, -19, 33, -67, 105, -171, 305, -515, 857, -1467, 2497, -4211, 7145, -12139, 20561, -34851, 59129, -100251, 169953, -288211, 488713, -828619, 1405041, -2382467, 4039705, ...

MCS1622368 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = - A_N-1 - 2 A_N-3 (score: 5)

2, 3, -5, -1, 16, -12, -68, 140, 336, -1456, -1568, 16128, 1120, -194656, 180096, 2545088, -5246528, -35474880, 124665856, 513881984, -2882533248, -7395106432, 67928304640, 94764036864, ...

MCS864306 : A₀ = 2; A₁ = 3; A_K+1 = - A_K - K A_K-1 (score: 5)

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

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

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

MCS1574434 : A₀ = 2; A₁ = 3; A₂ = 5; A_N = - A_N-3 (score: 5)

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

MCS865026 : A₀ = 2; A₁ = 3; A_N = - A_N-1 - A_N-2 (score: 4)

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

2, 3, -5, 2, -6, 10, -13, 18, -29, 41, -60, 88, -130, 189, -278, 407, -597, 874, -1282, 1878, -2753, 4034, -5913, 8665, -12700, 18612, -27278, 39977, -58590, 85867, -125845, 184434, -270302, ...

MCS1683552 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = - A_N-1 - A_N-3 - 1 (score: 5)

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

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

2, -3, -5, 4, 13, -3, -30, -7, 63, 44, -119, -151, 194, 421, -237, -1036, 53, 2309, 930, -4671, -4169, 8412, 13009, -12655, -34430, 12301, 81515, 9828, -175331, -101171, 340834, 377673, -580497, ...

MCS6336902 : A₀ = 1; A₁ = 1; A₂ = 2; A_N = - 2 A_N-2 - A_N-3 (score: 5)

2, -3, -5, 5, 9, -11, -19, 21, 37, -43, -75, 85, 149, -171, -299, 341, 597, -683, -1195, 1365, 2389, -2731, -4779, 5461, 9557, -10923, -19115, 21845, 38229, -43691, -76459, 87381, 152917, -174763, ...

MCS877248 : A₀ = 1; A₁ = 2; A_N = - 2 A_N-2 - 1 (score: 4)

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

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

2, 3, 5, 6, 8, 8, 10, 9, 12, 10, 15, 11, 19, 11, 24, 9, 31, 4, 42, -6, 60, -25, 90, -60, 141, -123, 229, -235, 382, -433, 649, -782, 1116, -1396, 1934, -2475, 3368, -4370, 5883, -7697, 10295, ...

MCS25462326 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = A_K-1 - A_K-2 + K (score: 5)

2, 3, 5, 6, 9, 9, 14, 11, 21, 10, 33, 1, 58, -29, 117, -114, 265, -343, 646, -949, 1637, -2542, 4225, -6719, 10994, -17661, 28709, -46314, 75081, -121335, 196478, -317749, 514293, -831974, ...

MCS6924806 : A₀ = 1; A₁ = 1; A_K+1 = - A_K + A_K-1 + 2 K (score: 5)

2, -3, -5, -6, -13, -17, -20, -29, -35, -40, -51, -59, -66, -79, -89, -98, -113, -125, -136, -153, -167, -180, -199, -215, -230, -251, -269, -286, -309, -329, -348, -373, -395, -416, -443, -467, ...

MCS6381830 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K-2 - 2 K (score: 5)

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

MCS26209 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = - A_K-2 - K - 1 (score: 5)

2, 3, 5, 7, 9, 10, 10, 9, 8, 8, 10, 14, 19, 23, 24, 21, 15, 9, 7, 12, 24, 39, 50, 50, 36, 12, -11, -19, -2, 39, 89, 123, 117, 62, -26, -107, -132, -68, 78, 250, 359, 323, 116, -199, -477, -547, ...

MCS6439302 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K - A_K-2 + K (score: 5)

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

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

floor(N(N-1)/6) (A1840)

2, 3, -5, -7, 9, 13, -19, -27, 37, 53, -75, -107, 149, 213, -299, -427, 597, 853, -1195, -1707, 2389, 3413, -4779, -6827, 9557, 13653, -19115, -27307, 38229, 54613, -76459, -109227, 152917, ...

MCS3508994 : A₀ = 2; A₁ = 3; A_N = - 2 A_N-2 - 1 (score: 5)

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

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

1 + floor(N²/4) (A33638)

2, -3, 5, -7, 10, -15, 22, -32, 47, -69, 101, -148, 217, -318, 466, -683, 1001, -1467, 2150, -3151, 4618, -6768, 9919, -14537, 21305, -31224, 45761, -67066, 98290, -144051, 211117, -309407, ...

MCS6489622 (alias MCS6489653) : A₀ = 1; A₁ = 0; A₂ = 1; A_N = - A_N-1 - A_N-3 (score: 5)

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

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

2, 3, -5, 7, -16, 57, -269, 1557, -10630, 83483, -740717, 7323687, -79819840, 950514393, -12276867269, 170925627373, ...

MCS855426 : A₀ = 2; A₁ = 3; A_K+1 = - K A_K - A_K-1 (score: 5)

2, 3, -5, -8, -2, 8, 4, -13, -20, 0, 23, 9, -35, -45, 12, 65, 17, -94, -100, 58, 174, 21, -254, -218, 209, 447, -17, -683, -458, 671, 1111, -244, -1814, -900, 2024, 2679, -1160, -4740, -1557, ...

MCS1600608 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = - A_K-1 - A_K-2 - K (score: 5)

2, 3, -5, -8, 7, 12, -19, -30, 31, 52, -71, -114, 131, 216, -275, -446, 535, 876, -1087, -1770, 2155, 3520, -4331, -7062, 8639, 14100, -17303, -28226, 34579, 56424, -69187, -112878, 138343, ...

MCS3435266 : A₀ = 2; A₁ = 3; A_K+1 = - 2 A_K-1 - K (score: 5)

2, 3, -5, -8, 7, 21, -6, -49, -9, 104, 67, -199, -238, 331, 675, -424, -1681, 173, 3786, 1335, -7745, -6456, 14155, 20657, -21854, -55469, 23051, 132792, 9367, -288635, -151526, 567903, 591687, ...

MCS1584224 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = - 2 A_N-2 - A_N-3 (score: 5)

2, 3, -5, -8, -11, -5, -4, -3, -11, -14, -17, -11, -10, -9, -17, -20, -23, -17, -16, -15, -23, -26, -29, -23, -22, -21, -29, -32, -35, -29, -28, -27, -35, -38, -41, -35, -34, -33, -41, -44, -47, ...

MCS1595488 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = - A_K-2 - 2 K (score: 5)

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

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

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

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

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

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

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

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

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

MCS12864 (alias MCS1646656, MCS1646657, MCS6586637)

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

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

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

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

MCS844 (alias MCS864774, MCS3459094) : A₀ = 0; A₁ = 1; A_N = - A_N-1 + A_N-2 (score: 3)

Signed Fibonacci numbers, or F_-n (A39834)

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

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

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

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

Fibonacci numbers (A0045)

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

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

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

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

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

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

MCS252546 (alias MCS6933250) : A₀ = 2; A_N = 2 A_N-1 - 1 (score: 4)

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

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

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

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

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

2, 3, -5, -11, 17, 60, -91, -437, 668, 4024, -6243, -44932, 70892, 590359, -947556, -8926277, 14570537, 152694265, -253343389, -2915761572, 4914173515, 61484336401, -105196055758, ...

MCS393648 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = - K A_K-1 - A_K-2 (score: 5)

2, 3, -5, -11, -19, -20, -25, -30, -44, -56, -70, -77, -88, -99, -119, -137, -157, -170, -187, -204, -230, -254, -280, -299, -322, -345, -377, -407, -439, -464, -493, -522, -560, -596, -634, -665, ...

MCS394080 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = - A_K-2 - K² (score: 5)

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

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

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

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

2, 3, -5, -11, 26, 67, -181, -535, 1630, 5351, -17929, -64211, 233078, 898955, -3496169, -14383279, 59434874, 258899023, -1129262605, -5177980459, 23714514706, 113915570099, -545433838237, ...

MCS1736813 : A₀ = -1; A₁ = -1; A_K+1 = - K A_K-1 + 1 (score: 5)

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

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

2, 3, -5, 12, -21, 37, -62, 103, -169, 276, -449, 729, -1182, 1915, -3101, 5020, -8125, 13149, -21278, 34431, -55713, 90148, -145865, 236017, -381886, 617907, -999797, 1617708, -2617509, 4235221, ...

MCS1617984 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = - 2 A_N-1 + A_N-3 (score: 5)

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

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

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

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

2, -3, 5, -16, 63, -316, 1895, -13266, 106127, -955144, 9551439, -105065830, 1260789959, -16390269468, 229463772551, ...

MCS505442 : A₀ = 2; A_K+1 = - K A_K - A_K - 1 (score: 5)

2, 3, -5, 17, -65, 320, -1903, 13256, -105728, 949649, -9483234, 104209846, -1249568503, 16234907305, -227184492424, ...

MCS394816 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = - K A_K + A_K-2 (score: 5)

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

MCS1625184 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = - A_N-1 - A_N-2 - A_N-3 (score: 5)

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

MCS3463938 : A₀ = 2; A₁ = 3; A_K+1 = - A_K - A_K-1 - K (score: 5)

2, 3, -6, 1, -8, 9, -16, 17, -34, 41, -68, 91, -144, 199, -304, 433, -648, 935, -1386, 2015, -2970, 4335, -6372, 9319, -13678, 20025, -29370, 43021, -63074, 92415, -135466, 198509, -290956, ...

MCS1628256 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = - A_K - A_K-2 - K (score: 5)

2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, -6, 2, 3, ...

MCS3519234 : A₀ = 2; A₁ = 3; A_N = - A_N-1 - A_N-2 - 1 (score: 5)

2, -3, -6, -3, -2, -7, -10, -7, -6, -11, -14, -11, -10, -15, -18, -15, -14, -19, -22, -19, -18, -23, -26, -23, -22, -27, -30, -27, -26, -31, -34, -31, -30, -35, -38, -35, -34, -39, -42, -39, -38, ...

MCS857792 : A₀ = 1; A₁ = 2; A_K+1 = - A_K-1 - 2 K (score: 4)

2, -3, -6, -3, 4, 3, -8, -15, -4, 13, 8, -21, -34, -1, 40, 19, -56, -77, 18, 113, 38, -153, -174, 91, 302, 57, -420, -387, 334, 777, 22, -1143, -832, 1087, 1940, -291, -3064, -1687, 3316, 4711, ...

MCS25009 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = - A_K-1 - A_K-2 - K (score: 5)

2, -3, -6, 3, 8, -11, -22, 15, 36, -39, -82, 67, 152, -147, -318, 279, 620, -575, -1258, 1131, 2496, -2283, -5014, 4543, 10004, -9111, -20034, 18195, 40040, -36419, -80110, 72807, 160188, -145647, ...

MCS858816 : A₀ = 1; A₁ = 2; A_K+1 = - 2 A_K-1 - K (score: 4)

2, 3, 6, 6, 9, 7, 11, 7, 14, 7, 19, 6, 26, 2, 36, -7, 52, -24, 79, -55, 125, -111, 204, -211, 341, -388, 580, -700, 998, -1249, 1730, -2214, 3013, -3909, 5263, -6885, 9210, -12109, 16135, -21278, ...

MCS6365581 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = A_K-1 - A_K-2 + K (score: 5)

2, -3, -6, 7, 22, -37, -134, 257, 1070, -2315, -10702, 25463, 128422, -331021, -1797910, 4965313, 28766558, -84410323, -517798046, 1603796135, 10355960918, -33679718837, -227831140198, ...

MCS874508 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 - 2 (score: 5)

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

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

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

MCS428289 (alias MCS869505, MCS3499137, MCS3510789)

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

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

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

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

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

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

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

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

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

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

MCS427968 : A₀ = 1; A₁ = 2; A_N = - 3 A_N-2 (score: 4)

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

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

MCS1711874 : A₀ = 2; A₁ = 3; A_N = - 3 A_N-2 (score: 5)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2, -3, 6, -13, 24, -51, 98, -201, 396, -799, 1590, -3189, 6368, -12747, 25482, -50977, 101940, -203895, 407774, -815565, 1631112, -3262243, 6524466, -13048953, 26097884, -52195791, 104391558, ...

MCS31405 (alias MCS2004674) : A₀ = 0; A_K+1 = - 2 A_K - K + 2 (score: 5)

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

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

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

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

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

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

2, 3, -7, 1, 13, -15, -11, 41, -19, -63, 101, 25, -227, 177, 277, -631, 77, 1185, -1339, -1031, 3709, -1647, -5771, 9065, 2477, -20607, 15653, 25561, -56867, 5745, 107989, -119479, -96499, 335457, ...

MCS3459842 : A₀ = 2; A₁ = 3; A_N = - A_N-1 - 2 A_N-2 (score: 5)

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

2, -3, -7, 5, 23, -31, -145, 209, 1151, -1891, -11521, 20789, 138239, -270271, -1935361, 4054049, 30965759, -68918851, -557383681, 1309458149, 11147673599, -27498621151, -245248819201, ...

MCS878092 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 - K - 1 (score: 5)

2, -3, -7, -7, -10, -19, -27, -31, -38, -51, -63, -71, -82, -99, -115, -127, -142, -163, -183, -199, -218, -243, -267, -287, -310, -339, -367, -391, -418, -451, -483, -511, -542, -579, -615, -647, ...

MCS877360 : A₀ = 1; A₁ = 2; A_K+1 = - A_K-1 - K² - 1 (score: 5)

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

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

2, -3, -7, 10, 38, -53, -276, 386, 2537, -3584, -28293, 40471, 371393, -538301, -5611366, 8241423, 95931523, -142734248, -1830940360, 2758753437, 38592481808, -58861635254, -890385835021, ...

MCS1574598 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - K A_K-1 - A_K-2 (score: 5)

2, -3, -7, 11, 34, -67, -239, 535, 2150, -5351, -23651, 64211, 307462, -898955, -4611931, 14383279, 78402826, -258899023, -1489653695, 5177980459, 31282727594, -113915570099, -719502734663, ...

MCS877324 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K-1 - A_K-1 - 1 (score: 5)

2, -3, 7, -12, 21, -35, 58, -95, 155, -252, 409, -663, 1074, -1739, 2815, -4556, 7373, -11931, 19306, -31239, 50547, -81788, 132337, -214127, 346466, -560595, 907063, -1467660, 2374725, -3842387, ...

MCS6471942 : A₀ = 1; A₁ = 1; A₂ = 2; A_N = - 2 A_N-1 + A_N-3 (score: 5)

2, 3, -7, 12, -27, 61, -134, 295, -651, 1436, -3167, 6985, -15406, 33979, -74943, 165292, -364563, 804069, -1773430, 3911423, -8626915, 19027260, -41965943, 92558801, -204144862, 450255667, ...

MCS1618016 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = - 2 A_N-1 - A_N-3 (score: 5)

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

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

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

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

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

MCS501122 : A₀ = 2; A_N = - 2 A_N-1 + 1 (score: 4)

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

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

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

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

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

2, 3, 7, 13, 36, 79, 253, 633, 2278, 6331, 25059, 75973, 325768, 1063623, 4886521, 17017969, 83070858, 306323443, 1578346303, 6126468861, 33145272364, 134782314943, 762341264373, ...

MCS54320 (alias MCS3476518) : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 - A_K-1 + 1 (score: 5)

2, 3, 7, 13, 36, 79, 253, 633, 2278, 6331, 25059, 75973, 325768, 1063623, 4886521, 17017969, 83070858, 306323443, 1578346303, 6126468861, 33145272364, 134782314943, 762341264373, ...

MCS868390 : A₀ = 1; A₁ = 1; A_K+1 = K A_K-1 + 1 (score: 4)

2, 3, 7, 13, 36, 79, 253, 633, 2278, 6331, 25059, 75973, 325768, 1063623, 4886521, 17017969, 83070858, 306323443, 1578346303, 6126468861, 33145272364, 134782314943, 762341264373, ...

MCS868872 : A₀ = 1; A₁ = 2; A_K+1 = K A_K-1 + A_K-1 + 1 (score: 5)

2, 3, 7, 14, 38, 91, 280, 766, 2611, 7940, 29487, 97891, 391271, 1399961, 5966956, 22790647, 102838213, 416198602, 1976716694, 8426810253, 41927249176, 187366542260, 972753541301, ...

MCS1574022 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = K A_K-1 + A_K-2 (score: 5)

2, 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, 1261482359, ...

MCS806976 : A₀ = 1; A₁ = 2; A₂ = 3; A_N = 2 A_N-1 + A_N-3 (score: 5)

2, 3, 7, 16, 44, 124, 388, 1256, 4360, 15664, 59264, 231568, 942736, 3953120, 17151424, 76448224, 350871008, 1650490816, 7966168960, 39325494464, 198648873664, ...

MCS215048 : A₀ = 1; A₁ = 2; A_K+1 = A_K + K A_K-1 (score: 4)

2, 3, 7, 18, 47, 123, 322, 843, 2207, 5778, 15127, 39603, 103682, 271443, 710647, 1860498, 4870847, 12752043, 33385282, 87403803, 228826127, 599074578, 1568397607, 4106118243, 10749957122, ...

MCS1733378 : A₀ = 2; A₁ = 3; A_N = 3 A_N-1 - A_N-2 (score: 6)

Bisection of Lucas numbers (A5248)

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

2, 3, -7, 19, -79, 402, -2431, 17096, -137170, 1236961, -12386706, 136390936, -1637928193, 21305453215, -298412735946, ...

MCS394848 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = - K A_K - A_K-2 (score: 5)

2, 3, 7, 22, 89, 446, 2677, 18740, 149921, 1349290, 13492901, 148421912, 1781062945, 23153818286, 324153456005, ...

MCS500802 : A₀ = 2; A_K+1 = K A_K + A_K + 1 (score: 5)

2, 3, 7, 23, 95, 482, 2915, 20500, 164482, 1483253, 14853030, 163547812, 1964056997, 25547593991, 357829863686, ...

MCS394304 : A₀ = 1; A₁ = 2; A₂ = 3; A_K+1 = K A_K + A_K-2 (score: 5)

2, -3, 7, -25, 118, -683, 4663, -36621, 324926, -3212639, 35014103, -416956597, 5385421658, -74978946615, ...

MCS1710861 : A₀ = -1; A₁ = -1; A_K+1 = - K A_K - A_K-1 (score: 5)

2, 3, 7, 25, 118, 683, 4663, 36621, 324926, 3212639, 35014103, 416956597, 5385421658, 74978946615, ...

MCS860992 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + A_K - A_K-1 (score: 5)

2, -3, -8, -3, 0, -19, -36, -11, 8, -59, -116, -3, 88, -163, -372, 101, 488, -491, -1300, 621, 2200, -1683, -4884, 2837, 9192, -6299, -19060, 11869, 37336, -24579, -75572, 48197, 150120, -97483, ...

MCS854832 : A₀ = 1; A₁ = 2; A_K+1 = - 2 A_K-1 - K² (score: 5)

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