Minimally Complex Sequences  


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2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20, -22, -24, -26, -28, -30, -32, -34, -36, -38, -40, -42, -44, -46, -48, -50, -52, -54, -56, -58, -60, -62, -64, -66, -68, -70, -72, -74, -76, -78, ...

MCS14165 (alias MCS503042) : AK = - 2 K + 2 (score: 4)

2, 0, -2, -4, -9, -17, -28, -45, -71, -109, -165, -248, -370, -549, -812, -1198, -1764, -2594, -3811, -5595, -8210, -12043, -17661, -25895, -37963, -55650, -81572, -119563, -175242, -256844, ...

MCS12592 : A0 = 0; A1 = 1; A2 = 2; AK+1 = AK + AK-2 - K (score: 5)

2, 0, -2, -5, -6, -5, -1, 4, 8, 8, 3, -6, -15, -19, -14, 0, 18, 31, 30, 11, -21, -52, -64, -44, 7, 70, 113, 105, 34, -80, -186, -221, -142, 43, 263, 404, 360, 96, -309, -670, -767, -459, 210, 976, ...

MCS6717830 : A0 = 1; A1 = 1; A2 = 2; AN = AN-1 - AN-3 - 1 (score: 5)

2, 0, -2, -6, -6, -2, 10, 22, 26, 6, -38, -90, -102, -26, 154, 358, 410, 102, -614, -1434, -1638, -410, 2458, 5734, 6554, 1638, -9830, -22938, -26214, -6554, 39322, 91750, 104858, 26214, -157286, ...

MCS6423942 : A0 = 1; A1 = 1; A2 = 2; AN = AN-1 - 2 AN-3 (score: 5)

2, 0, -2, -8, -30, -128, -650, -3912, -27398, -219200, -1972818, -19728200, -217010222, -2604122688, -33853594970, -473950329608, ...

MCS494402 : A0 = 2; AK+1 = K AK - 2 K (score: 5)

2, 0, -2, -9, -18, -34, -54, -83, -118, -164, -218, -285, -362, -454, -558, -679, -814, -968, -1138, -1329, -1538, -1770, -2022, -2299, -2598, -2924, -3274, -3653, -4058, -4494, -4958, -5455, ...

MCS213552 : A0 = 1; A1 = 2; AK+1 = AK-1 - K2 (score: 4)

2, 0, -3, 1, 13, -4, -77, 29, 617, -260, -6169, 2861, 74029, -37192, -1036405, 557881, 16582481, -9483976, -298484657, 180195545, 5969693141, -3784106444, -131333249101, 87034448213, ...

MCS217100 : A0 = 1; A1 = 2; AK+1 = - K AK-1 + 1 (score: 4)

2, 0, -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, ...

MCS792705 (alias MCS1585413, MCS3170829, MCS3170841, MCS6341677, MCS12683373)

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

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

MCS435040 : A0 = 0; A1 = 2; AK+1 = - AK-1 - K + 1 (score: 5)

2, 0, -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, ...

MCS396385 (alias MCS792773, MCS3171097, MCS6342197)

A0 = 0; A1 = 0; A2 = 1; AN = - AN-2 - AN-3 (score: 4)

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

MCS878784 : A0 = 1; A1 = 2; AN = AN-1 - AN-2 - 1 (score: 4)

2, 0, -3, -5, -2, 6, 13, 9, -10, -32, -31, 11, 74, 94, 9, -159, -262, -112, 309, 683, 486, -506, -1675, -1655, 526, 3856, 4985, 603, -8238, -13826, -6191, 15873, 35890, 26208, -25555, -87653, ...

MCS6435206 : A0 = 1; A1 = 1; A2 = 2; AN = AN-1 - AN-2 - AN-3 (score: 5)

2, 0, -3, -6, 0, 9, 18, 0, -27, -54, 0, 81, 162, 0, -243, -486, 0, 729, 1458, 0, -2187, -4374, 0, 6561, 13122, 0, -19683, -39366, 0, 59049, 118098, 0, -177147, -354294, 0, 531441, 1062882, 0, ...

MCS12303 : A0 = 0; A1 = 1; A2 = 2; AN = - 3 AN-3 (score: 5)

2, 0, -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, ...

MCS2012354 : A0 = 2; AK+1 = AK - K - 2 (score: 5)

2, 0, -3, -10, -38, -181, -1049, -7163, -56256, -499142, -4935165, -53787674, -640516924, -8272932339, -115180535823, ...

MCS877376 : A0 = 1; A1 = 2; AK+1 = K AK - AK-1 - 1 (score: 5)

2, 0, -4, 0, 8, 0, -16, 0, 32, 0, -64, 0, 128, 0, -256, 0, 512, 0, -1024, 0, 2048, 0, -4096, 0, 8192, 0, -16384, 0, 32768, 0, -65536, 0, 131072, 0, -262144, 0, 524288, 0, -1048576, 0, 2097152, 0, ...

MCS106848 (alias MCS427393, MCS854789) : A0 = 0; A1 = 2; AN = - 2 AN-2 (score: 4)

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

2, 0, -4, 0, 16, 0, -96, 0, 768, 0, -7680, 0, 92160, 0, -1290240, 0, 20643840, 0, -371589120, 0, 7431782400, 0, -163499212800, 0, ...

MCS26630 : A0 = 0; A1 = 2; AK+1 = - K AK-1 (score: 4)

2, 0, -4, 2, 22, -10, -152, 82, 1370, -818, -15068, 9818, 195886, -137450, -2938288, 2199202, 49950898, -39585634, -949067060, 791712682, 19930408262, -17417679002, -458399390024, 418024296050, ...

MCS54529 : A0 = 0; A1 = 1; AK+1 = - K AK-1 + 2 (score: 5)

2, 0, -4, 5, 30, -28, -232, 261, 2330, -2860, -27948, 37193, 391286, -557880, -6260560, 9483977, 112690098, -180195544, -2253801940, 3784106445, 49583642702, -87034448212, ...

MCS214029 : A0 = 0; A1 = 0; AK+1 = - K AK-1 + K (score: 4)

2, 0, -4, 8, -8, 0, 16, -32, 32, 0, -64, 128, -128, 0, 256, -512, 512, 0, -1024, 2048, -2048, 0, 4096, -8192, 8192, 0, -16384, 32768, -32768, 0, 65536, -131072, 131072, 0, -262144, 524288, ...

MCS26981 : A0 = 0; A1 = 1; AN = - 2 AN-1 - 2 AN-2 (score: 5)

A108520

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

2, 0, -4, -4, 4, 12, 4, -20, -28, 12, 68, 44, -92, -180, 4, 364, 356, -372, -1084, -340, 1828, 2508, -1148, -6164, -3868, 8460, 16196, -724, -33116, -31668, 34564, 97900, 28772, -167028, -224572, ...

MCS860864 : A0 = 1; A1 = 2; AN = AN-1 - 2 AN-2 (score: 4)

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

2, 0, -4, -7, -7, -5, -4, -6, -10, -13, -13, -11, -10, -12, -16, -19, -19, -17, -16, -18, -22, -25, -25, -23, -22, -24, -28, -31, -31, -29, -28, -30, -34, -37, -37, -35, -34, -36, -40, -43, -43, ...

MCS861888 : A0 = 1; A1 = 2; AK+1 = AK - AK-1 - K (score: 4)

2, 0, -4, -10, -15, -17, -14, -7, 1, 5, 1, -12, -30, -45, -48, -34, -6, 24, 39, 25, -20, -81, -129, -133, -77, 26, 132, 181, 126, -36, -248, -406, -403, -189, 182, 549, 701, 481, -107, -848, ...

MCS25185 : A0 = 0; A1 = 1; A2 = 2; AK+1 = AK - AK-2 - K (score: 5)

2, 0, -4, -10, -18, -28, -40, -54, -70, -88, -108, -130, -154, -180, -208, -238, -270, -304, -340, -378, -418, -460, -504, -550, -598, -648, -700, -754, -810, -868, -928, -990, -1054, -1120, ...

MCS28333 : AK = - K2 - K + 2 (score: 5)

2, 0, -4, -12, -40, -176, -976, -6480, -49888, -436032, -4260544, -45993920, -543405952, -6972289536, -96525241600, ...

MCS854848 : A0 = 1; A1 = 2; AK+1 = K AK - 2 AK-1 (score: 5)

2, 0, -4, -15, -60, -290, -1686, -11519, -90474, -802756, -7937096, -86505311, -1030126648, -13305141126, -185241849130, ...

MCS858944 : A0 = 1; A1 = 2; AK+1 = K AK - AK-1 - K (score: 5)

2, 0, -5, -6, 13, 42, -37, -332, -37, 2950, 3319, -29132, -68961, 309754, 1275207, -3371104, -23774417, 33534350, 461473855, -175678796, -9405155897, -5715901182, 201197528551, 332663255736, ...

MCS878604 : A0 = 1; A1 = 2; AK+1 = AK - K AK-1 - 1 (score: 5)

2, 0, -5, -13, -24, -38, -55, -75, -98, -124, -153, -185, -220, -258, -299, -343, -390, -440, -493, -549, -608, -670, -735, -803, -874, -948, -1025, -1105, -1188, -1274, -1363, -1455, -1550, ...

MCS1001968 : A0 = 1; AK+1 = AK - 3 K + 1 (score: 5)

2, 0, -6, 0, 18, 0, -54, 0, 162, 0, -486, 0, 1458, 0, -4374, 0, 13122, 0, -39366, 0, 118098, 0, -354294, 0, 1062882, 0, -3188646, 0, 9565938, 0, -28697814, 0, 86093442, 0, -258280326, 0, ...

MCS213984 : A0 = 0; A1 = 2; AN = - 3 AN-2 (score: 5)

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

2, 0, -6, 0, 30, 0, -210, 0, 1890, 0, -20790, 0, 270270, 0, -4054050, 0, 68918850, 0, -1309458150, 0, 27498621150, 0, -632468286450, 0, ...

MCS106886 : A0 = 0; A1 = 2; AK+1 = - K AK-1 - AK-1 (score: 5)

2, 0, -6, 6, 24, -60, -108, 588, 384, -6264, 2040, 73128, -99648, -924144, 2418864, 12367440, -53488128, -169125792, 1185400224, 2197115616, -27090520320, -21246023232, 644327990592, ...

MCS1728621 : A0 = -1; A1 = -1; AK+1 = - AK - K AK-1 (score: 5)

2, 0, -6, -6, 24, 60, -108, -588, 384, 6264, 2040, -73128, -99648, 924144, 2418864, -12367440, -53488128, 169125792, 1185400224, -2197115616, -27090520320, 21246023232, 644327990592, 134423433024, ...

MCS860940 : A0 = 1; A1 = 2; AK+1 = AK - K AK-1 - AK-1 (score: 5)

2, 0, -6, -9, 11, 51, -21, -385, -225, 3231, 5471, -30081, -95745, 295295, 1635711, -2793729, -28965121, 18528255, 539900415, 187863551, -10610144769, -14555279361, 218867905535, 553639330815, ...

MCS861708 : A0 = 1; A1 = 2; AK+1 = AK - K AK-1 - K (score: 5)

2, 0, -6, -15, -25, -35, -46, -60, -78, -99, -121, -143, -166, -192, -222, -255, -289, -323, -358, -396, -438, -483, -529, -575, -622, -672, -726, -783, -841, -899, -958, -1020, -1086, -1155, ...

MCS860976 : A0 = 1; A1 = 2; AK+1 = AK - AK-1 - K2 (score: 5)

2, 0, -6, -16, -30, -48, -70, -96, -126, -160, -198, -240, -286, -336, -390, -448, -510, -576, -646, -720, -798, -880, -966, -1056, -1150, -1248, -1350, -1456, -1566, -1680, -1798, -1920, -2046, ...

MCS28325 : AK = - 2 K2 + 2 (score: 5)

2, 0, -6, -27, -70, -152, -286, -495, -798, -1224, -1798, -2555, -3526, -4752, -6270, -8127, -10366, -13040, -16198, -19899, -24198, -29160, -34846, -41327, -48670, -56952, -66246, -76635, -88198, ...

MCS213528 : A0 = 1; A1 = 2; AK+1 = AK-1 - K3 (score: 5)

2, 0, -7, -6, 37, 80, -215, -934, 1217, 11492, -3111, -152506, -108951, 2178640, 3921857, -33115022, -103708447, 525476972, 2599645913, -8435370498, -65627580583, 128385940872, ...

MCS870413 : A0 = 0; A1 = 0; AK+1 = AK - K AK-1 + 1 (score: 5)

2, 0, -8, 0, 48, 0, -384, 0, 3840, 0, -46080, 0, 645120, 0, -10321920, 0, 185794560, 0, -3715891200, 0, 81749606400, 0, ...

MCS213045 : A0 = 0; A1 = -1; AK+1 = - K AK-1 (score: 4)

2, 0, -8, 0, 48, 0, -384, 0, 3840, 0, -46080, 0, 645120, 0, -10321920, 0, 185794560, 0, -3715891200, 0, 81749606400, 0, ...

MCS427545 : A0 = -1; A1 = 0; AK+1 = - K AK-1 - AK-1 (score: 5)

2, 0, -8, 0, 64, 0, -768, 0, 12288, 0, -245760, 0, 5898240, 0, -165150720, 0, 5284823040, 0, -190253629440, 0, ...

MCS106518 : A0 = 0; A1 = 2; AK+1 = - 2 K AK-1 (score: 5)

2, 0, -8, -8, 56, 136, -536, -2440, 6136, 50056, -72664, -1173896, 570040, 31091336, 15130216, -917609864, -1401776776, 29796958600, 80260922536, ...

MCS860204 : A0 = 1; A1 = 2; AK+1 = AK - 2 K AK-1 (score: 5)

2, 0, -8, 40, -192, 1064, -6976, 53208, -462320, 4500232, -48454944, 571411256, -7321388368, 101249656680, ...

MCS853558 : A0 = 1; A1 = 1; AK+1 = - K AK - K AK-1 (score: 5)

2, 0, -8, -16, 0, 64, 128, 0, -512, -1024, 0, 4096, 8192, 0, -32768, -65536, 0, 262144, 524288, 0, -2097152, -4194304, 0, 16777216, 33554432, 0, -134217728, -268435456, 0, 1073741824, 2147483648, ...

MCS53911 : A0 = 0; A1 = 1; AN = 2 AN-1 - 4 AN-2 (score: 7)

Horadam sequence Wn(0, 1; -4, 2), Lucas sequence Un(2, 4)

2, 0, 12, 0, 120, 0, 1680, 0, 30240, 0, 665280, 0, 17297280, 0, 518918400, 0, 17643225600, 0, 670442572800, 0, ...

MCS1704278 : A0 = 1; A1 = 0; AK+1 = 2 K AK-1 (score: 5)

2, 0, 12, -40, 270, -1848, 14840, -133488, 1334970, -14684560, 176214852, -2290792920, 32071101062, -481066515720, ...

MCS7734 (alias MCS123752) : A0 = 0; AK+1 = - K AK + K2 - K (score: 5)

2, 0, -12, 0, 120, 0, -1680, 0, 30240, 0, -665280, 0, 17297280, 0, -518918400, 0, 17643225600, 0, -670442572800, 0, ...

MCS426073 : A0 = -1; A1 = 0; AK+1 = - 2 K AK-1 (score: 5)

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

MCS6685740 : A0 = 1; A1 = 2; A2 = 1; AN = AN-3 - 1 (score: 5)

2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, ...

MCS3409 (alias MCS12568, MCS436416, MCS6982678)

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

1 + cos(Nπ/2) (A7877)

2, 1, 0, 1, 4, 1, -14, 1, 106, 1, -944, 1, 10396, 1, -135134, 1, 2027026, 1, -34459424, 1, 654729076, 1, -13749310574, 1, 316234143226, 1, ...

MCS856588 : A0 = 1; A1 = 2; AK+1 = - K AK-1 + AK-1 + K (score: 5)

2, 1, 0, 1, 4, 5, 2, -1, 2, 9, 10, 1, -6, 3, 20, 19, -6, -21, 6, 47, 36, -31, -60, 19, 116, 67, -108, -155, 70, 293, 116, -331, -376, 249, 742, 163, -954, -867, 830, 1861, 78, -2649, -1896, 2615, ...

MCS24881 : A0 = 0; A1 = 1; A2 = 2; AK+1 = - AK-1 - AK-2 + K (score: 5)

2, 1, 0, 1, 4, 7, 8, 7, 6, 7, 10, 13, 14, 13, 12, 13, 16, 19, 20, 19, 18, 19, 22, 25, 26, 25, 24, 25, 28, 31, 32, 31, 30, 31, 34, 37, 38, 37, 36, 37, 40, 43, 44, 43, 42, 43, 46, 49, 50, 49, 48, ...

MCS3515584 : A0 = 1; A1 = 2; AK+1 = AK - AK-1 + K - 1 (score: 5)

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

MCS15657 : A0 = 0; AK+1 = - K AK + 2 AK + 1 (score: 5)

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

MCS125208 : A0 = 1; AK+1 = - K AK + AK + 1 (score: 4)

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

MCS125026 : A0 = 2; AK+1 = - K AK + 1 (score: 4)

2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, ...

MCS786966 (alias MCS6295702) : A0 = 0; A1 = 2; A2 = 1; AN = AN-3 (score: 5)

2, 1, 0, 2, 2, -1, 1, 4, -1, -2, 6, 2, -7, 5, 10, -11, -4, 22, -6, -25, 29, 20, -53, 10, 74, -62, -63, 137, 2, -199, 136, 202, -334, -65, 537, -268, -601, 806, 334, -1406, 473, 1741, -1878, -1267, ...

MCS6566150 : A0 = 1; A1 = 1; A2 = 2; AN = - AN-2 + AN-3 + 1 (score: 5)

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

MCS107104 : A0 = 0; A1 = 2; AK+1 = - AK-1 + K (score: 4)

2, 1, 0, 2, -1, 1, 1, -2, 3, -2, 0, 3, -5, 5, -2, -3, 8, -10, 7, 1, -11, 18, -17, 6, 12, -29, 35, -23, -6, 41, -64, 58, -17, -47, 105, -122, 75, 30, -152, 227, -197, 45, 182, -379, 424, -242, ...

MCS6489132 : A0 = 1; A1 = 2; A2 = 1; AN = - AN-1 + AN-3 (score: 5)

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

MCS3461893 : A0 = 0; A1 = -1; AK+1 = - AK - AK-1 + K (score: 5)

2, 1, 0, 3, 2, -3, 4, 7, -10, 1, 24, -21, -22, 69, -20, -113, 158, 73, -384, 243, 530, -1011, -44, 2071, -1978, -2159, 6120, -1797, -10438, 14037, 6844, -34913, 21230, 48601, -91056, -6141, ...

MCS3170950 : A0 = 1; A1 = 1; A2 = 2; AN = - AN-2 + 2 AN-3 (score: 5)

2, 1, 0, 3, 6, 1, -4, 7, 18, -3, -24, 19, 62, -23, -108, 63, 234, -107, -448, 235, 918, -447, -1812, 919, 3650, -1811, -7272, 3651, 14574, -7271, -29116, 14575, 58266, -29115, -116496, 58267, ...

MCS856769 (alias MCS27173, MCS3510977) : A0 = 0; A1 = 0; AK+1 = - 2 AK-1 + K (score: 4)

2, 1, 0, 3, 8, -5, -36, 49, 304, -423, -3020, 4675, 36264, -60749, -507668, 911265, 8122720, -15491471, -146208924, 294337987, 2924178520, -6181097685, -64331927396, 142165246801, ...

MCS428556 : A0 = 1; A1 = 2; AK+1 = - K AK-1 + 2 K (score: 5)

2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, 0, -1, 0, 1, 2, 1, ...

MCS6401 (alias MCS819393, MCS1638789, MCS6555180)

A0 = 0; A1 = 1; A2 = 2; AN = - AN-3 + 1 (score: 4)

2, 1, 0, -1, 0, 3, 0, -15, 0, 105, 0, -945, 0, 10395, 0, -135135, 0, 2027025, 0, -34459425, 0, 654729075, 0, -13749310575, 0, 316234143225, 0, ...

MCS427276 : A0 = 1; A1 = 2; AK+1 = - K AK-1 + 2 AK-1 (score: 5)

2, 1, 0, -1, -2, -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, ...

MCS3541 (alias MCS126210) : AK = - K + 2 (score: 3)

2, 1, 0, -1, -4, -19, -110, -751, -5898, -52331, -517412, -5639201, -67153000, -867349799, -12075744186, -180268812991, ...

MCS213824 : A0 = 1; A1 = 2; AK+1 = K AK - AK-1 (score: 4)

2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, ...

MCS787217 (alias MCS787222) : A0 = -1; A1 = 0; A2 = 2; AN = - AN-3 (score: 5)

2, 1, 0, -2, -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, ...

MCS1606022 (alias MCS6424108) : A0 = 1; A1 = 1; A2 = 2; AN = AN-1 - AN-3 (score: 4)

2, 1, 0, -3, -2, -3, 4, 1, 10, -7, 8, -27, 22, -43, 76, -87, 162, -239, 336, -563, 814, -1235, 1940, -2863, 4410, -6743, 10136, -15563, 23622, -35835, 54748, -83079, 126418, -192575, 292576, ...

MCS24709 : A0 = 0; A1 = 1; A2 = 2; AN = AN-2 - 2 AN-3 (score: 5)

2, 1, 0, -3, -8, -17, -32, -57, -98, -165, -274, -451, -738, -1203, -1956, -3175, -5148, -8341, -13508, -21869, -35398, -57289, -92710, -150023, -242758, -392807, -635592, -1028427, -1664048, ...

MCS3516032 : A0 = 1; A1 = 2; AK+1 = AK + AK-1 - K - 1 (score: 5)

2, 1, 0, -5, -12, -25, -42, -67, -98, -139, -188, -249, -320, -405, -502, -615, -742, -887, -1048, -1229, -1428, -1649, -1890, -2155, -2442, -2755, -3092, -3457, -3848, -4269, -4718, -5199, -5710, ...

MCS856624 : A0 = 1; A1 = 2; AK+1 = AK-1 - K2 + K (score: 5)

2, 1, 0, -7, -16, -39, -68, -127, -200, -335, -500, -791, -1144, -1751, -2484, -3727, -5224, -7743, -10772, -15847, -21944, -32135, -44372, -64799, -89320, -130223, -179316, -261175, -359416, ...

MCS427312 : A0 = 1; A1 = 2; AK+1 = 2 AK-1 - K2 (score: 5)

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

MCS14032986 : A0 = 2; A1 = 1; AN = AN-2 - 1 (score: 5)

2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, ...

MCS413745 (alias MCS3309958) : A0 = 0; A1 = 1; A2 = 1; AN = - AN-3 + 2 (score: 5)

2, 1, 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, ...

MCS13836378 : A0 = 2; A1 = 1; AN = - AN-1 + AN-2 (score: 5)

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

2, 1, 1, 0, -1, -3, -6, -11, -19, -32, -53, -87, -142, -231, -375, -608, -985, -1595, -2582, -4179, -6763, -10944, -17709, -28655, -46366, -75023, -121391, -196416, -317809, -514227, -832038, ...

MCS3500160 : A0 = 1; A1 = 2; AN = AN-1 + AN-2 - 2 (score: 5)

2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

MCS500322 (alias MCS500546) : A0 = 2; AK+1 = - K AK + K + 1 (score: 5)

2, 1, 1, 1, 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, ...

MCS223944794 : A0 = 2; A1 = 1; AK+1 = AK-1 + K - 2 (score: 7)

Quarter-squares plus 1: floor(N2/4)+1 (A33638)

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

MCS26177 (alias MCS6358572) : A0 = 0; A1 = 1; A2 = 2; AK+1 = - AK-2 + K - 1 (score: 5)

2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, ...

MCS393478 (alias MCS1573932, MCS25183066) : A0 = 1; A1 = 1; A2 = 2; AN = AN-3 (score: 3)

A simple period-3 sequence. (A100063)

2, 1, 1, 2, 2, 2, 3, 4, 5, 7, 10, 14, 20, 29, 42, 61, 89, 130, 190, 278, 407, 596, 873, 1279, 1874, 2746, 4024, 5897, 8642, 12665, 18561, 27202, 39866, 58426, 85627, 125492, 183917, 269543, ...

MCS13120 : A0 = 0; A1 = 1; A2 = 2; AN = AN-1 + AN-3 - 1 (score: 5)

2, 1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, ...

MCS504962 : A0 = 2; AK+1 = AK + K - 1 (score: 4)

2, 1, 1, 2, 7, 34, 203, 1420, 11359, 102230, 1022299, 11245288, 134943455, 1754264914, 24559708795, 368395631924, ...

MCS504898 : A0 = 2; AK+1 = K AK + AK - 1 (score: 5)

2, 1, 1, 3, 1, 1, 5, 1, 1, 9, 1, 1, 17, 1, 1, 33, 1, 1, 65, 1, 1, 129, 1, 1, 257, 1, 1, 513, 1, 1, 1025, 1, 1, 2049, 1, 1, 4097, 1, 1, 8193, 1, 1, 16385, 1, 1, 32769, 1, 1, 65537, 1, 1, 131073, 1, ...

MCS3342982 : A0 = 1; A1 = 1; A2 = 2; AN = 2 AN-3 - 1 (score: 5)

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

MCS1638665 (alias MCS3486913, MCS6554677, MCS13847574, MCS26218710)

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

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

MCS869568 (alias MCS1713673, MCS7022093) : A0 = 1; A1 = 2; AK+1 = - AK-1 + K + 1 (score: 4)

2, 1, 1, 4, 12, 27, 51, 86, 134, 197, 277, 376, 496, 639, 807, 1002, 1226, 1481, 1769, 2092, 2452, 2851, 3291, 3774, 4302, 4877, 5501, 6176, 6904, 7687, 8527, 9426, 10386, 11409, 12497, 13652, ...

MCS504866 : A0 = 2; AK+1 = AK + K2 - 1 (score: 5)

2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, 1, -1, 0, 0, 2, 1, ...

MCS1638793 (alias MCS3277593) : A0 = 0; A1 = 0; A2 = 2; AN = - AN-3 + 1 (score: 5)

2, 1, 1, -1, 0, -2, 1, -2, 3, -3, 5, -6, 8, -11, 14, -19, 25, -33, 44, -58, 77, -102, 135, -179, 237, -314, 416, -551, 730, -967, 1281, -1697, 2248, -2978, 3945, -5226, 6923, -9171, 12149, -16094, ...

MCS6177 (alias MCS6325804) : A0 = 0; A1 = 1; A2 = 2; AN = AN-2 - AN-3 (score: 4)

2, 1, 1, -1, 4, -17, 89, -551, 3946, -32119, 293017, -2962289, 32878196, -397500641, 5200386529, -73202912047, ...

MCS860768 : A0 = 1; A1 = 2; AK+1 = - K AK + AK + AK-1 (score: 5)

2, 1, 1, -1, -2, -5, -7, -11, -14, -19, -23, -29, -34, -41, -47, -55, -62, -71, -79, -89, -98, -109, -119, -131, -142, -155, -167, -181, -194, -209, -223, -239, -254, -271, -287, -305, -322, -341, ...

MCS870016 (alias MCS6986246, MCS13738074) : A0 = 1; A1 = 2; AK+1 = AK-1 - K + 1 (score: 4)

2, 1, 1, -1, -4, -10, -20, -37, -65, -111, -186, -308, -506, -827, -1347, -2189, -3552, -5758, -9328, -15105, -24453, -39579, -64054, -103656, -167734, -271415, -439175, -710617, -1149820, ...

MCS430912 : A0 = 0; A1 = 2; AK+1 = AK + AK-1 - K (score: 5)

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

MCS25191258 : A0 = 2; A1 = 1; A2 = 1; AN = - AN-3 (score: 5)

2, 1, 2, 0, 2, -1, 3, -2, 5, -4, 8, -8, 13, -15, 22, -27, 38, -48, 66, -85, 115, -150, 201, -264, 352, -464, 617, -815, 1082, -1431, 1898, -2512, 3330, -4409, 5843, -7738, 10253, -13580, 17992, ...

MCS820273 (alias MCS1640545, MCS6562182, MCS6562189)

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

2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...

MCS53376 (alias MCS63328, MCS253314, MCS3416154)

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

A simple periodic sequence (A0034)

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

2, 1, 2, 1, 4, 3, 6, 1, 4, -1, 10, 5, 16, -5, 6, -15, 28, 7, 50, -35, 8, -77, 94, 9, 180, -161, 10, -331, 352, 11, 694, -671, 12, -1353, 1378, 13, 2744, -2717, 14, -5447, 5476, 15, 10938, -10907, ...

MCS794801 : A0 = 0; A1 = 1; A2 = 1; AK+1 = - 2 AK-2 + K (score: 5)

2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, ...

MCS6295642 : A0 = 2; A1 = 1; A2 = 2; AN = AN-3 (score: 5)

2, 1, 2, 2, 2, 3, 3, 4, 5, 6, 8, 10, 13, 17, 22, 29, 38, 50, 66, 87, 115, 152, 201, 266, 352, 466, 617, 817, 1082, 1433, 1898, 2514, 3330, 4411, 5843, 7740, 10253, 13582, 17992, 23834, 31573, ...

MCS6693126 : A0 = 1; A1 = 1; A2 = 2; AN = AN-2 + AN-3 - 1 (score: 5)

2, 1, 2, 2, 3, 4, 6, 9, 14, 22, 35, 56, 90, 145, 234, 378, 611, 988, 1598, 2585, 4182, 6766, 10947, 17712, 28658, 46369, 75026, 121394, 196419, 317812, 514230, 832041, 1346270, 2178310, 3524579, ...

MCS439360 : A0 = 0; A1 = 2; AN = AN-1 + AN-2 - 1 (score: 5)

2, 1, 2, 2, 4, 4, 5, 4, 5, 5, 7, 7, 8, 7, 8, 8, 10, 10, 11, 10, 11, 11, 13, 13, 14, 13, 14, 14, 16, 16, 17, 16, 17, 17, 19, 19, 20, 19, 20, 20, 22, 22, 23, 22, 23, 23, 25, 25, 26, 25, 26, 26, 28, ...

MCS1589638 : A0 = 1; A1 = 1; A2 = 2; AK+1 = - AK-2 + K (score: 4)

2, 1, 2, 2, 6, 8, 30, 48, 210, 384, 1890, 3840, 20790, 46080, 270270, 645120, 4054050, 10321920, 68918850, 185794560, 1309458150, 3715891200, 27498621150, 81749606400, 632468286450, ...

MCS3408474 : A0 = 2; A1 = 1; AK+1 = K AK-1 (score: 5)

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

MCS3200 (alias MCS6761, MCS819329, MCS819333, MCS1638661, MCS6554646, MCS6554668)

A0 = 0; A1 = 1; A2 = 2; AN = AN-3 + 1 (score: 4)

Two Steps Forward, One Step Back (A8611)

2, 1, 2, 3, 3, 5, 6, 8, 11, 14, 19, 25, 33, 44, 58, 77, 102, 135, 179, 237, 314, 416, 551, 730, 967, 1281, 1697, 2248, 2978, 3945, 5226, 6923, 9171, 12149, 16094, 21320, 28243, 37414, 49563, ...

MCS25301174 : A0 = 1; A1 = 1; A2 = 0; AN = AN-2 + AN-3 (score: 5)

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

MCS3148332 : A0 = 1; A1 = 2; A2 = 1; AN = 2 AN-3 (score: 5)

2, 1, 2, 4, 5, 7, 11, 16, 23, 34, 50, 73, 107, 157, 230, 337, 494, 724, 1061, 1555, 2279, 3340, 4895, 7174, 10514, 15409, 22583, 33097, 48506, 71089, 104186, 152692, 223781, 327967, 480659, ...

MCS6423596 : A0 = 1; A1 = 2; A2 = 1; AN = AN-1 + AN-3 (score: 5)

2, 1, 2, 5, 4, 3, 8, 9, 4, 9, 16, 7, 6, 23, 16, -1, 24, 35, -6, 9, 62, 7, -30, 79, 62, -83, 44, 173, -98, -99, 302, 33, -368, 303, 436, -635, -96, 1109, -500, -1165, 1650, 707, -2772, 987, 3524, ...

MCS12440 : A0 = 0; A1 = 1; A2 = 2; AK+1 = - AK-1 + AK-2 + K (score: 5)

2, 1, 2, 5, 6, 5, 6, 9, 10, 9, 10, 13, 14, 13, 14, 17, 18, 17, 18, 21, 22, 21, 22, 25, 26, 25, 26, 29, 30, 29, 30, 33, 34, 33, 34, 37, 38, 37, 38, 41, 42, 41, 42, 45, 46, 45, 46, 49, 50, 49, 50, ...

MCS428736 : A0 = 1; A1 = 2; AK+1 = - AK-1 + 2 K (score: 4)

2, 1, 2, 5, 10, 17, 26, 37, 50, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 325, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 1025, 1090, 1157, 1226, 1297, 1370, 1445, ...

MCS1009986 : A0 = 2; AK+1 = AK + 2 K - 1 (score: 5)

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

MCS124994 (alias MCS250657) : A0 = 2; AK+1 = K AK + 1 (score: 4)

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

MCS501136 : A0 = 1; AK+1 = K AK - 2 AK + 1 (score: 5)


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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.
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    Sequences Beginning 3,8,... ; 3,9,... ; etc.
    Sequences Beginning 4,0,... ; 4,1,... ; etc.
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