Minimally Complex Sequences  


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3, -2, -3, 5, 1, -8, 4, 9, -12, -5, 21, -7, -26, 28, 19, -54, 9, 73, -63, -64, 136, 1, -200, 135, 201, -335, -66, 536, -269, -602, 805, 333, -1407, 472, 1740, -1879, -1268, 3619, -611, -4887, ...

MCS396353 (alias MCS792709, MCS25366742) : A0 = 0; A1 = 0; A2 = 1; AN = - AN-2 + AN-3 (score: 4)

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

MCS877316 : A0 = 1; A1 = 3; AN = - AN-2 - 1 (score: 4)

3, -2, -4, -1, 6, 5, -5, -11, 0, 16, 11, -16, -27, 5, 43, 22, -48, -65, 26, 113, 39, -139, -152, 100, 291, 52, -391, -343, 339, 734, 4, -1073, -738, 1069, 1811, -331, -2880, -1480, 3211, 4360, ...

MCS6342182 : A0 = 1; A1 = 1; A2 = 3; AN = - AN-2 - AN-3 (score: 5)

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

MCS99864 : A0 = 0; A1 = 1; A2 = 3; AK+1 = - AK-2 - K (score: 5)

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

MCS858884 : A0 = 1; A1 = 3; AK+1 = - AK-1 - K (score: 4)

3, -2, -6, 4, 12, -8, -24, 16, 48, -32, -96, 64, 192, -128, -384, 256, 768, -512, -1536, 1024, 3072, -2048, -6144, 4096, 12288, -8192, -24576, 16384, 49152, -32768, -98304, 65536, 196608, -131072, ...

MCS854788 : A0 = 1; A1 = 3; AN = - 2 AN-2 (score: 4)

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

3, -2, -7, 5, 27, -26, -163, 181, 1303, -1630, -13031, 17929, 156371, -233078, -2189195, 3496169, 35027119, -59434874, -630488143, 1129262605, 12609762859, -23714514706, -277414782899, ...

MCS876596 : A0 = 1; A1 = 3; AK+1 = - K AK-1 - 1 (score: 5)

3, -2, -7, -7, -9, -18, -27, -31, -37, -50, -63, -71, -81, -98, -115, -127, -141, -162, -183, -199, -217, -242, -267, -287, -309, -338, -367, -391, -417, -450, -483, -511, -541, -578, -615, -647, ...

MCS855236 : A0 = 1; A1 = 3; AK+1 = - AK-1 - K2 (score: 5)

3, -2, -8, 3, 28, -20, -174, 133, 1384, -1206, -13850, 13255, 166188, -172328, -2326646, 2584905, 37226320, -43943402, -670073778, 834924619, 13401475540, -17533417020, -294832461902, ...

MCS858164 : A0 = 1; A1 = 3; AK+1 = - K AK-1 - K (score: 5)

3, -2, -9, 8, 45, -48, -315, 384, 2835, -3840, -31185, 46080, 405405, -645120, -6081075, 10321920, 103378275, -185794560, -1964187225, 3715891200, 41247931725, -81749606400, -948702429675, ...

MCS855092 : A0 = 1; A1 = 3; AK+1 = - K AK-1 - AK-1 (score: 5)

3, -2, 15, -24, 115, -282, 1203, -3740, 15771, -56910, 246163, -985992, 4432275, -19222154, 90138555, -416915172, 2039409163, -9960797430, 50748980691, -259925726720, ...

MCS54464 : A0 = 0; A1 = 1; AK+1 = - AK + K AK-1 + 1 (score: 5)

3, -2, -11, 11, 67, -76, -535, 685, 5351, -7534, -64211, 97943, 898955, -1469144, -14383279, 24975449, 258899023, -474533530, -5177980459, 9965204131, 113915570099, -229199695012, ...

MCS868405 : A0 = 0; A1 = -1; AK+1 = - K AK-1 + 1 (score: 5)

3, -2, -12, 12, 96, -120, -1152, 1680, 18432, -30240, -368640, 665280, 8847360, -17297280, -247726080, 518918400, 7927234560, -17643225600, -285380444160, 670442572800, ...

MCS852148 : A0 = 1; A1 = 3; AK+1 = - 2 K AK-1 (score: 5)

3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

MCS124483 : A0 = 3; AK+1 = K AK - AK (score: 5)

3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, 0, 3, -3, ...

MCS432514 : A0 = 0; A1 = 3; AN = - AN-1 - AN-2 (score: 5)

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

3, -3, 1, 2, -5, 6, -4, -1, 7, -11, 10, -3, -8, 18, -21, 13, 5, -26, 39, -34, 8, 31, -65, 73, -42, -23, 96, -138, 115, -19, -119, 234, -253, 134, 100, -353, 487, -387, 34, 453, -840, 874, -421, ...

MCS6489141 : A0 = 0; A1 = -1; A2 = -1; AN = - AN-1 + AN-3 (score: 5)

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

MCS3486468 : A0 = 1; A1 = 3; AN = - AN-1 - AN-2 + 1 (score: 5)

3, -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, ...

MCS498371 : A0 = 3; AK+1 = - AK - 2 K (score: 5)

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

MCS3461892 : A0 = 1; A1 = 3; AK+1 = - AK - AK-1 + K (score: 5)

3, -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, ...

MCS124611 : A0 = 3; AK+1 = - AK - K (score: 4)

3, -3, 2, -5, 8, -10, 15, -23, 33, -48, 71, -104, 152, -223, 327, -479, 702, -1029, 1508, -2210, 3239, -4747, 6957, -10196, 14943, -21900, 32096, -47039, 68939, -101035, 148074, -217013, 318048, ...

MCS101400 : A0 = 0; A1 = 1; A2 = 3; AN = - AN-1 - AN-3 (score: 5)

3, -3, 2, -6, -3, -13, -12, -24, -25, -39, -42, -58, -63, -81, -88, -108, -117, -139, -150, -174, -187, -213, -228, -256, -273, -303, -322, -354, -375, -409, -432, -468, -493, -531, -558, -598, ...

MCS124467 : A0 = 3; AK+1 = - AK - K2 (score: 5)

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

MCS31107 : A0 = 3; AN = - AN-1 (score: 3)

3, -3, 4, 0, 9, 7, 18, 18, 31, 33, 48, 52, 69, 75, 94, 102, 123, 133, 156, 168, 193, 207, 234, 250, 279, 297, 328, 348, 381, 403, 438, 462, 499, 525, 564, 592, 633, 663, 706, 738, 783, 817, 864, ...

MCS124451 : A0 = 3; AK+1 = - AK + K2 (score: 5)

3, -3, 4, -1, -2, 6, -7, 5, 1, -8, 13, -12, 4, 9, -21, 25, -16, -5, 30, -46, 41, -11, -35, 76, -87, 52, 24, -111, 163, -139, 28, 135, -274, 302, -167, -107, 409, -576, 469, -60, -516, 985, -1045, ...

MCS101392 : A0 = 0; A1 = 1; A2 = 3; AN = - AN-1 + AN-3 (score: 5)

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

MCS124547 : A0 = 3; AK+1 = - AK + K (score: 4)

3, -3, 4, -10, 10, -25, 29, -61, 82, -152, 224, -387, 599, -999, 1584, -2598, 4166, -6781, 10929, -17729, 28638, -46388, 75004, -121415, 196395, -317835, 514204, -832066, 1346242, -2178337, ...

MCS3463684 : A0 = 1; A1 = 3; AK+1 = - AK + AK-1 - K (score: 5)

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

MCS249155 : A0 = 3; AK+1 = - AK + 2 K (score: 5)

3, -3, 5, -7, 11, -15, 23, -33, 49, -71, 105, -153, 225, -329, 483, -707, 1037, -1519, 2227, -3263, 4783, -7009, 10273, -15055, 22065, -32337, 47393, -69457, 101795, -149187, 218645, -320439, ...

MCS26412598 : A0 = 1; A1 = 1; A2 = 1; AN = - AN-1 - AN-3 + 1 (score: 5)

3, -3, 5, -9, 13, -23, 35, -59, 93, -153, 245, -399, 643, -1043, 1685, -2729, 4413, -7143, 11555, -18699, 30253, -48953, 79205, -128159, 207363, -335523, 542885, -878409, 1421293, -2299703, ...

MCS3518980 : A0 = 1; A1 = 3; AN = - AN-1 + AN-2 - 1 (score: 5)

3, -3, 6, -9, 15, -24, 39, -63, 102, -165, 267, -432, 699, -1131, 1830, -2961, 4791, -7752, 12543, -20295, 32838, -53133, 85971, -139104, 225075, -364179, 589254, -953433, 1542687, -2496120, ...

MCS432386 : A0 = 0; A1 = 3; AN = - AN-1 + AN-2 (score: 5)

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

3, -3, 6, -18, 72, -360, 2160, -15120, 120960, -1088640, 10886400, -119750400, 1437004800, -18681062400, 261534873600, ...

MCS124515 : A0 = 3; AK+1 = - K AK - AK (score: 5)

3, -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, ...

MCS6972429 : A0 = -1; A1 = -1; AN = - AN-1 + AN-2 + 1 (score: 5)

3, -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, ...

MCS3957 : A0 = 0; AN = - 2 AN-1 + 3 (score: 5)

3, -3, -1, 9, -5, -11, 23, 1, -45, 45, 47, -135, 43, 229, -313, -143, 771, -483, -1057, 2025, 91, -4139, 3959, 4321, -12237, 3597, 20879, -28071, -13685, 69829, -42457, -97199, 182115, 12285, ...

MCS396369 : A0 = 0; A1 = 1; A2 = 1; AN = - AN-2 + 2 AN-3 (score: 5)

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

MCS6391334 : A0 = 1; A1 = 1; A2 = 3; AK+1 = - AK-2 - K (score: 5)

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

MCS3498756 : A0 = 1; A1 = 3; AN = - AN-2 - 2 (score: 5)

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

MCS3513092 : A0 = 1; A1 = 3; AK+1 = - AK-1 - K - 1 (score: 5)

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, 218453, ...

MCS3508996 : A0 = 1; A1 = 3; AN = - 2 AN-2 - 1 (score: 5)

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

MCS3431172 : A0 = 1; A1 = 3; AK+1 = - AK-1 - 2 K (score: 5)

3, -3, -8, 3, 12, -11, -30, 15, 52, -39, -114, 67, 216, -147, -446, 279, 876, -575, -1770, 1131, 3520, -2283, -7062, 4543, 14100, -9111, -28226, 18195, 56424, -36419, -112878, 72807, 225724, ...

MCS3435268 : A0 = 1; A1 = 3; AK+1 = - 2 AK-1 - K (score: 5)

3, -3, -8, 8, 1, -25, 14, 26, -65, 1, 116, -132, -115, 363, -150, -594, 875, 293, -2064, 1456, 2649, -5585, 262, 10882, -11433, -10359, 33196, -12508, -53915, 78899, 28898, -186730, 128899, ...

MCS27061 : A0 = 0; A1 = 1; AK+1 = - AK - 2 AK-1 - K (score: 5)

3, -3, -9, 9, 27, -27, -81, 81, 243, -243, -729, 729, 2187, -2187, -6561, 6561, 19683, -19683, -59049, 59049, 177147, -177147, -531441, 531441, 1594323, -1594323, -4782969, 4782969, 14348907, ...

MCS1711876 : A0 = 1; A1 = 3; AN = - 3 AN-2 (score: 5)

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

3, -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, ...

MCS31578 : A0 = 0; AK+1 = - 2 AK + 2 K - 1 (score: 5)

3, -3, 13, -24, 67, -151, 377, -896, 2179, -5243, 12677, -30584, 73859, -178287, 430449, -1039168, 2508803, -6056755, 14622333, -35301400, 85225155, -205751687, 496728553, -1199208768, 2895146115, ...

MCS13816326 : A0 = 1; A1 = 1; AK+1 = - 2 AK + AK-1 + K (score: 5)

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

MCS865028 : A0 = 1; A1 = 3; AN = - AN-1 - AN-2 (score: 4)

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

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

MCS505539 : A0 = 3; AK+1 = - AK - K - 1 (score: 5)

3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, 3, -4, ...

MCS126339 : A0 = 3; AN = - AN-1 - 1 (score: 4)

3, -4, 3, -6, 10, -13, 19, -29, 42, -61, 90, -132, 193, -283, 415, -608, 891, -1306, 1914, -2805, 4111, -6025, 8830, -12941, 18966, -27796, 40737, -59703, 87499, -128236, 187939, -275438, 403674, ...

MCS6489638 : A0 = 1; A1 = 1; A2 = 3; AN = - AN-1 - AN-3 (score: 5)

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

MCS505475 : A0 = 3; AK+1 = - AK + K - 1 (score: 5)

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

MCS6745 (alias MCS1726849) : A0 = 0; A1 = 1; AN = - 2 AN-1 - AN-2 (score: 4)

A181983

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

3, -4, 5, -9, 12, -18, 26, -39, 56, -83, 121, -178, 260, -382, 559, -820, 1201, -1761, 2580, -3782, 5542, -8123, 11904, -17447, 25569, -37474, 54920, -80490, 117963, -172884, 253373, -371337, ...

MCS841777 : A0 = 0; A1 = 1; A2 = 1; AN = - AN-1 - AN-3 - 1 (score: 5)

3, -4, 5, -11, 39, -184, 1065, -7271, 57103, -506656, 5009457, -54597371, 650158995, -8397469564, 116914414901, ...

MCS855428 : A0 = 1; A1 = 3; AK+1 = - K AK - AK-1 (score: 5)

3, -4, 6, -9, 13, -19, 28, -41, 60, -88, 129, -189, 277, -406, 595, -872, 1278, -1873, 2745, -4023, 5896, -8641, 12664, -18560, 27201, -39865, 58425, -85626, 125491, -183916, 269542, -395033, ...

MCS405601 (alias MCS1622405, MCS3244825, MCS25958582)

A0 = 0; A1 = 0; A2 = 1; AN = - AN-1 - AN-3 (score: 4)

3, -4, -2, 14, -6, -64, 100, 348, -1148, -1984, 13464, 8360, -169928, 61248, 2317744, -3236464, -33847440, 88867328, 520386592, -2208865824, -8198866016, 54585048320, 125790004032, ...

MCS864308 : A0 = 1; A1 = 3; AK+1 = - AK - K AK-1 (score: 5)

3, -4, 11, -18, 41, -76, 159, -310, 629, -1248, 2507, -5002, 10017, -20020, 40055, -80094, 160205, -320392, 640803, -1281586, 2563193, -5126364, 10252751, -20505478, 41010981, -82021936, ...

MCS1002305 : A0 = -1; AK+1 = - 2 AK + K + 1 (score: 5)

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

MCS3463940 : A0 = 1; A1 = 3; AK+1 = - AK - AK-1 - K (score: 5)

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

MCS3519236 : A0 = 1; A1 = 3; AN = - AN-1 - AN-2 - 1 (score: 5)

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

MCS503171 : A0 = 3; AN = - AN-1 - 2 (score: 5)

3, -5, 5, -9, 9, -15, 17, -25, 31, -43, 55, -75, 97, -131, 171, -229, 301, -401, 529, -703, 929, -1233, 1631, -2163, 2863, -3795, 5025, -6659, 8819, -11685, 15477, -20505, 27161, -35983, 47665, ...

MCS26773046 : A0 = 1; A1 = 1; A2 = 1; AN = AN-2 - AN-3 - 1 (score: 5)

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

MCS6907405 : A0 = -1; A1 = -1; AN = - 2 AN-1 - AN-2 (score: 5)

Horadam sequence Wn(-1, -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, ...

MCS432385 (alias MCS864773, MCS1729545, MCS1729549)

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

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

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

MCS25887798 : A0 = 1; A1 = 1; A2 = 1; AN = - 2 AN-1 + AN-3 (score: 5)

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, ...

MCS3459844 : A0 = 1; A1 = 3; AN = - AN-1 - 2 AN-2 (score: 5)

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

3, -5, -4, 7, -2, -12, 8, 9, -21, -2, 29, -20, -32, 48, 11, -81, 36, 91, -118, -56, 208, -63, -265, 270, 201, -536, 68, 736, -605, -669, 1340, 63, -2010, 1276, 2072, -3287, -797, 5358, -2491, ...

MCS1674305 : A0 = 0; A1 = 0; A2 = 1; AN = - AN-2 + AN-3 - 1 (score: 5)

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

MCS1957 (alias MCS3378, MCS125280, MCS250561, MCS501123)

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

A77925

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

3, -5, 13, -31, 75, -181, 437, -1055, 2547, -6149, 14845, -35839, 86523, -208885, 504293, -1217471, 2939235, -7095941, 17131117, -41358175, 99847467, -241053109, 581953685, -1404960479, ...

MCS3453444 : A0 = 1; A1 = 3; AN = - 2 AN-1 + AN-2 (score: 5)

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

3, -5, 21, -95, 555, -3783, 29717, -263661, 2606903, -28412261, 338340241, -4370010859, 60841811799, -908257166111, ...

MCS3427718 : A0 = 1; A1 = 1; AK+1 = - K AK - AK-1 + K (score: 5)

3, -5, 29, -129, 799, -5557, 44505, -400481, 4004891, -44053701, 528644533, -6872378785, 96213303159, ...

MCS124520 : A0 = 1; AK+1 = - K AK - AK + K2 (score: 5)

3, -6, 5, -9, 7, -12, 9, -15, 11, -18, 13, -21, 15, -24, 17, -27, 19, -30, 21, -33, 23, -36, 25, -39, 27, -42, 29, -45, 31, -48, 33, -51, 35, -54, 37, -57, 39, -60, 41, -63, 43, -66, 45, -69, 47, ...

MCS26989 : A0 = 0; A1 = 1; AK+1 = - 2 AK - AK-1 - K (score: 5)

3, -6, 11, -24, 45, -94, 183, -372, 737, -1482, 2955, -5920, 11829, -23670, 47327, -94668, 189321, -378658, 757299, -1514616, 3029213, -6058446, 12116871, -24233764, 48467505, -96935034, ...

MCS497347 (alias MCS1002337) : A0 = 3; AK+1 = - 2 AK - K (score: 5)

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

MCS124291 : A0 = 3; AN = - 2 AN-1 (score: 4)

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, ...

MCS31446 (alias MCS497283) : A0 = 0; AK+1 = - 2 AK + K - 2 (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; AK+1 = K AK-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; AK+1 = - AK + K AK-1 (score: 4)

3, -6, 31, -156, 973, -6960, 56661, -516900, 5225671, -57999270, 701216923, -9173819256, 129134686521, ...

MCS13385 : A0 = 0; A1 = 1; AK+1 = - K AK + AK-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; AN = - AN-1 + AN-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, ...

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

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

MCS505219 : A0 = 3; AN = - 2 AN-1 - 1 (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; 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, ...

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

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

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

MCS54786 : A0 = 0; A1 = 1; AK+1 = 2 K AK-1 - 1 (score: 5)

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

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

3, -7, 31, -151, 911, -6371, 50975, -458767, 4587679, -50464459, 605573519, -7872455735, 110214380303, ...

MCS124568 : A0 = 1; AK+1 = - K AK - AK + K (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; AK+1 = - 2 AK - K (score: 3)

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

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

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

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

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

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

MCS1929 (alias MCS30872, MCS61745) : A0 = 0; AK+1 = - K AK + 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; AK+1 = - AK - AK-2 - K (score: 5)

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; AN = - 2 AN-1 - 3 (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; AN = - 3 AN-1 (score: 4)

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

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

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; AK+1 = AK-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 : AK = 2 K2 + K (score: 4)

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

Value of Fibonacci polynomials when x=3 (A6190)

Horadam sequence Wn(0, 1; 1, 3), Lucas sequence Un(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; AK+1 = 3 AK + K2 (score: 5)

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

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

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

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

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

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

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

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

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

MCS3442950 : A0 = 1; A1 = 1; AK+1 = K AK + AK + AK-1 (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; AK+1 = AK + 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; AK+1 = AK + 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 : AK = K3 + K + 1 (score: 5)

3, 11, 37, 117, 359, 1087, 3273, 9833, 29515, 88563, 265709, 797149, 2391471, 7174439, 21523345, 64570065, 193710227, 581130715, 1743392181, 5230176581, 15690529783, 47071589391, 141214768217, ...

MCS124752 : A0 = 1; AK+1 = 3 AK + 2 K (score: 5)

3, 11, 39, 139, 495, 1763, 6279, 22363, 79647, 283667, 1010295, 3598219, 12815247, 45642179, 162557031, 578955451, 2061980415, 7343852147, 26155517271, 93154256107, 331773802863, ...

MCS6770 : A0 = 0; A1 = 1; AN = 3 AN-1 + 2 AN-2 (score: 6)

A7482

Horadam sequence Wn(0, 1; 2, 3), Lucas sequence Un(3, -2)

3, 11, 43, 171, 683, 2731, 10923, 43691, 174763, 699051, 2796203, 11184811, 44739243, 178956971, 715827883, 2863311531, 11453246123, 45812984491, 183251937963, 733007751851, ...

MCS252640 : A0 = 1; AN = 4 AN-1 - 1 (score: 5)

(2(2N+1)+1)/3 (A7583)

3, 11, 43, 189, 971, 5863, 41091, 328793, 2959219, 29592291, 325515323, 3906184021, 50780392443, 710925494399, ...

MCS7812 (alias MCS125000) : A0 = 0; AK+1 = K AK + K2 + 1 (score: 5)

3, 11, 45, 219, 1275, 8713, 68437, 607229, 6003863, 65435275, 779219449, 10064417575, 140122626615, ...

MCS3427590 : A0 = 1; A1 = 1; AK+1 = K AK - AK-1 + K (score: 5)

3, 11, 47, 239, 1439, 10079, 80639, 725759, 7257599, 79833599, 958003199, 12454041599, 174356582399, ...

MCS124048 : A0 = 1; AK+1 = K AK + AK + K (score: 4)

3, 11, 48, 252, 1561, 11180, 91002, 830199, 8392993, 93153123, 1126230470, 14734149234, 207404319747, ...

MCS868929 : A0 = 0; A1 = 0; AK+1 = K AK + AK-1 + 1 (score: 5)

3, 11, 52, 301, 2055, 16139, 143196, 1415821, 15430835, 183754199, 2373373752, 33043478329, 493278801183, ...

MCS1710605 : A0 = -1; A1 = -1; AK+1 = K AK - AK-1 (score: 5)

3, 12, 27, 48, 75, 108, 147, 192, 243, 300, 363, 432, 507, 588, 675, 768, 867, 972, 1083, 1200, 1323, 1452, 1587, 1728, 1875, 2028, 2187, 2352, 2523, 2700, 2883, 3072, 3267, 3468, 3675, 3888, ...

MCS1763 : AK = 3 K2 (score: 4)


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Quick Index:
    Sequences Beginning 2,0,...
    Sequences Beginning 2,1,...
    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 3,0,... ; 3,1,... ; etc.
    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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