Minimally Complex Sequences

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2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568504, 2390480, 10349536, 46206736, 211799312, 997313824, 4809701440, 23758664096, 119952692896, 618884638912, ...

MCS860198 (alias MCS53808, MCS3443750) : A₀ = 1; A₁ = 1; A_K+1 = A_K + K A_K-1 (score: 4)

2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568504, 2390480, 10349536, 46206736, 211799312, 997313824, 4809701440, 23758664096, 119952692896, 618884638912, ...

MCS860680 : A₀ = 1; A₁ = 2; A_K+1 = A_K + K A_K-1 + A_K-1 (score: 5)

2, 4, 10, 32, 130, 652, 3914, 27400, 219202, 1972820, 19728202, 217010224, 2604122690, 33853594972, 473950329610, ...

MCS251280 : A₀ = 1; A_K+1 = K A_K - A_K + 2 (score: 5)

2, 4, 10, 32, 130, 652, 3914, 27400, 219202, 1972820, 19728202, 217010224, 2604122690, 33853594972, 473950329610, ...

MCS1960 (alias MCS62736, MCS125473) : A₀ = 0; A_K+1 = K A_K + 2 (score: 4)

2, 4, 11, 17, 28, 38, 53, 67, 86, 104, 127, 149, 176, 202, 233, 263, 298, 332, 371, 409, 452, 494, 541, 587, 638, 688, 743, 797, 856, 914, 977, 1039, 1106, 1172, 1243, 1313, 1388, 1462, 1541, ...

MCS249236 : A₀ = 1; A_K+1 = - A_K + 2 K² - K (score: 5)

2, 4, 11, 20, 36, 56, 85, 120, 166, 220, 287, 364, 456, 560, 681, 816, 970, 1140, 1331, 1540, 1772, 2024, 2301, 2600, 2926, 3276, 3655, 4060, 4496, 4960, 5457, 5984, 6546, 7140, 7771, 8436, 9140, ...

MCS3416598 : A₀ = 1; A₁ = 0; A_K+1 = A_K-1 + K² (score: 5)

2, 4, 11, 30, 95, 304, 1063, 3798, 14427, 56204, 229327, 959978, 4170555, 18570224, 85299103, 400992910, 1936376763, 9555242052, 48282777311, 248942860402, ...

MCS3514406 : A₀ = 1; A₁ = 1; A_K+1 = A_K + K A_K-1 - 1 (score: 5)

2, 4, 11, 38, 164, 859, 5319, 38093, 310064, 2828670, 28596765, 317393086, 3837313798, 50202472461, 706671928253, ...

MCS868928 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + A_K-1 + 1 (score: 5)

2, 4, 11, 41, 195, 1130, 7716, 60599, 537676, 5316162, 57940107, 689965123, 8911606493, 124072525780, ...

MCS6790 : A₀ = 0; A₁ = 1; A_K+1 = K A_K - A_K-1 + 1 (score: 5)

2, 4, 11, 42, 206, 1225, 8533, 68058, 611297, 6104437, 67080749, 804357691, 10450545546, 146240556895, ...

MCS6161 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = K A_K - A_K-2 (score: 5)

2, 4, 11, 42, 207, 1238, 8661, 69282, 623531, 6235302, 68588313, 823059746, 10699776687, 149796873606, ...

MCS500944 : A₀ = 1; A_K+1 = K A_K + A_K - K + 1 (score: 5)

2, -4, 11, -46, 234, -1415, 9951, -79842, 719993, -7209881, 79388533, -953382389, 12401180938, -173695921665, ...

MCS6169 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = - K A_K - A_K-2 (score: 5)

2, 4, 12, 24, 70, 156, 504, 1264, 4554, 12660, 50116, 151944, 651534, 2127244, 9773040, 34035936, 166141714, 612646884, 3156692604, 12252937720, 66290544726, 269564629884, ...

MCS428553 : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 + 2 K (score: 5)

2, -4, 12, -32, 88, -240, 656, -1792, 4896, -13376, 36544, -99840, 272768, -745216, 2035968, -5562368, 15196672, -41518080, 113429504, -309895168, 846649344, -2313089024, 6319476736, -17265131520, ...

MCS6907142 : A₀ = 1; A₁ = 1; A_N = - 2 A_N-1 + 2 A_N-2 (score: 5)

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

2, 4, -12, -32, 120, 384, -1680, -6144, 30240, 122880, -665280, -2949120, 17297280, 82575360, -518918400, -2642411520, 17643225600, 95126814720, -670442572800, ...

MCS1704301 : A₀ = -1; A₁ = -1; A_K+1 = - 2 K A_K-1 (score: 5)

2, 4, 12, 32, 120, 384, 1680, 6144, 30240, 122880, 665280, 2949120, 17297280, 82575360, 518918400, 2642411520, 17643225600, 95126814720, 670442572800, ...

MCS426070 : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K-1 (score: 4)

2, 4, 12, 36, 132, 492, 2076, 8964, 42180, 203532, 1047132, 5524836, 30656004, 174301740, 1032669852, 6261722052, 39307157316, 252205707084, ...

MCS430100 : A₀ = 1; A₁ = 2; A_K+1 = A_K + 2 K A_K-1 (score: 5)

2, 4, 12, 43, 188, 988, 6122, 43849, 356922, 3256156, 32918492, 365359579, 4417233452, 57789394468, 813468756018, ...

MCS856640 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + A_K-1 + K (score: 5)

2, 4, 12, 44, 200, 1088, 6928, 50672, 419232, 3874432, 39582784, 443159488, 5397079424, 71048351488, ...

MCS427328 : A₀ = 1; A₁ = 2; A_K+1 = K A_K + 2 A_K-1 (score: 5)

2, -4, 12, -48, 240, -1440, 10080, -80640, 725760, -7257600, 79833600, -958003200, 12454041600, -174356582400, ...

MCS497250 : A₀ = 2; A_K+1 = - K A_K - 2 A_K (score: 5)

2, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600, 174356582400, ...

MCS248386 : A₀ = 2; A_K+1 = K A_K + 2 A_K (score: 5)

2, 4, 13, 41, 106, 232, 449, 793, 1306, 2036, 3037, 4369, 6098, 8296, 11041, 14417, 18514, 23428, 29261, 36121, 44122, 53384, 64033, 76201, 90026, 105652, 123229, 142913, 164866, 189256, 216257, ...

MCS125188 : A₀ = 1; A_K+1 = A_K + K³ + 1 (score: 5)

2, -4, 13, -50, 246, -1463, 10191, -81282, 730075, -7290559, 80114867, -960648329, 12481137718, -174655813185, ...

MCS3084 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = - K A_K + A_K-2 (score: 5)

2, 4, 13, 54, 274, 1657, 11653, 93498, 843139, 8443043, 92966971, 1116446791, 14522251326, 203404485535, ...

MCS3080 : A₀ = 0; A₁ = 1; A₂ = 2; A_K+1 = K A_K + A_K-2 (score: 5)

2, 4, -14, -20, 14, 24, -46, -68, 70, 112, -166, -252, 302, 472, -638, -980, 1238, 1920, -2518, -3884, 4990, 7720, -10030, -15492, 20006, 30928, -40070, -61916, 80078, 123768, -160222, -247604, ...

MCS13724422 : A₀ = 1; A₁ = 1; A_K+1 = - 2 A_K-1 - 2 K (score: 5)

2, -4, 14, -40, 122, -364, 1094, -3280, 9842, -29524, 88574, -265720, 797162, -2391484, 7174454, -21523360, 64570082, -193710244, 581130734, -1743392200, 5230176602, -15690529804, 47071589414, ...

MCS7855 : A₀ = 0; A_N = - 3 A_N-1 + 2 (score: 5)

2, -4, 15, -70, 406, -2771, 21763, -193095, 1909188, -20807972, 247786477, -3200416228, 44558040716, -665170194511, ...

MCS3476870 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K - A_K-1 + 1 (score: 5)

2, -4, 23, -128, 880, -6904, 61265, -605736, 6601842, -78616356, 1015410799, -14137134816, 211041611456, ...

MCS856929 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K - A_K-1 + K (score: 5)

2, -4, 30, -232, 2330, -27948, 391286, -6260560, 112690098, -2253801940, 49583642702, ...

MCS15445 (alias MCS247128) : A₀ = 0; A_K+1 = - 2 K A_K + 2 K (score: 5)

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

MCS3520192 : A₀ = 1; A₁ = 2; A_K+1 = - A_K - A_K-1 - K - 1 (score: 5)

2, 5, 0, -5, 6, 17, -4, -25, 18, 61, -24, -109, 62, 233, -108, -449, 234, 917, -448, -1813, 918, 3649, -1812, -7273, 3650, 14573, -7272, -29117, 14574, 58265, -29116, -116497, 58266, 233029, ...

MCS27429 (alias MCS13708310) : A₀ = 0; A₁ = 1; A_K+1 = - 2 A_K-1 + K - 1 (score: 5)

2, -5, 0, 9, -10, -9, 28, -11, -46, 67, 24, -159, 110, 207, -428, 13, 842, -869, -816, 2553, -922, -4185, 6028, 2341, -14398, 9715, 19080, -38511, 350, 76671, -77372, -75971, 230714, -78773, ...

MCS3519168 : A₀ = 1; A₁ = 2; A_N = - A_N-1 - 2 A_N-2 - 1 (score: 5)

2, -5, -1, 0, -7, -3, -2, -9, -5, -4, -11, -7, -6, -13, -9, -8, -15, -11, -10, -17, -13, -12, -19, -15, -14, -21, -17, -16, -23, -19, -18, -25, -21, -20, -27, -23, -22, -29, -25, -24, -31, -27, ...

MCS3462848 : A₀ = 1; A₁ = 2; A_K+1 = - A_K - A_K-1 - 2 K (score: 5)

2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, ...

MCS786964 : A₀ = 1; A₁ = 2; A₂ = 5; A_N = A_N-3 (score: 5)

2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, -1, -2, -5, 1, 2, 5, ...

MCS787220 : A₀ = 1; A₁ = 2; A₂ = 5; A_N = - A_N-3 (score: 5)

2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, 1, 2, -5, ...

MCS3501248 : A₀ = 1; A₁ = 2; A_N = - A_N-1 - A_N-2 - 2 (score: 5)

2, -5, 1, -7, 7, -14, 14, -29, 34, -58, 76, -122, 167, -257, 364, -547, 787, -1169, 1697, -2504, 3652, -5371, 7852, -11528, 16874, -24752, 36253, -53155, 77878, -114161, 167285, -245195, 359323, ...

MCS6513030 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - A_K - A_K-2 - K (score: 5)

2, -5, -1, 8, -10, -11, 25, -10, -48, 59, 27, -156, 90, 209, -403, -30, 820, -777, -881, 2416, -674, -4179, 5505, 2830, -13864, 8179, 19523, -35908, -3166, 74953, -68651, -81286, 218556, -56017, ...

MCS3463872 : A₀ = 1; A₁ = 2; A_K+1 = - A_K - 2 A_K-1 - K (score: 5)

2, -5, -1, 16, -13, -35, 74, 31, -253, 160, 599, -1079, -718, 3955, -1801, -10064, 15467, 14725, -61126, 16951, 166427, -217280, -282001, 933841, -87838, -2713685, 2977199, 5163856, -14095453, ...

MCS1730496 : A₀ = 1; A₁ = 2; A_N = - A_N-1 - 3 A_N-2 (score: 5)

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

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

MCS1708074 : A₀ = 2; A₁ = 5; A_N = A_N-2 (score: 5)

Horadam sequence W_n(2, 5; 1, 0)

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

MCS1710122 : A₀ = 2; A₁ = 5; A_N = - A_N-2 (score: 5)

Horadam sequence W_n(2, 5; -1, 0)

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

MCS1015170 : A₀ = 2; A_N = - A_N-1 - 3 (score: 5)

2, 5, 4, 3, -2, 1, 4, 15, 10, 5, -16, -5, 6, 49, 28, 7, -78, -35, 8, 179, 94, 9, -332, -161, 10, 693, 352, 11, -1354, -671, 12, 2743, 1378, 13, -5448, -2717, 14, 10937, 5476, 15, -21830, -10907, ...

MCS25433654 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = - 2 A_K-2 + K (score: 5)

2, 5, 4, 3, 6, 9, 8, 7, 10, 13, 12, 11, 14, 17, 16, 15, 18, 21, 20, 19, 22, 25, 24, 23, 26, 29, 28, 27, 30, 33, 32, 31, 34, 37, 36, 35, 38, 41, 40, 39, 42, 45, 44, 43, 46, 49, 48, 47, 50, 53, 52, ...

MCS1714949 : A₀ = 0; A₁ = -1; A_K+1 = - A_K-1 + 2 K (score: 5)

2, 5, -5, 0, 16, -9, -15, 42, -2, -71, 87, 68, -228, 107, 365, -562, -150, 1293, -973, -1592, 3560, -353, -6743, 7474, 6038, -20959, 8911, 33036, -50828, -15213, 116901, -86442, -147326, 320245, ...

MCS13847302 : A₀ = 1; A₁ = 1; A_K+1 = - A_K - 2 A_K-1 + K (score: 5)

2, 5, 5, 4, 6, 9, 9, 8, 10, 13, 13, 12, 14, 17, 17, 16, 18, 21, 21, 20, 22, 25, 25, 24, 26, 29, 29, 28, 30, 33, 33, 32, 34, 37, 37, 36, 38, 41, 41, 40, 42, 45, 45, 44, 46, 49, 49, 48, 50, 53, 53, ...

MCS7023366 : A₀ = 1; A₁ = 1; A_K+1 = - A_K-1 + 2 K - 1 (score: 5)

2, -5, 5, -8, 9, -14, 16, -24, 29, -41, 52, -71, 92, -124, 162, -217, 285, -380, 501, -666, 880, -1168, 1545, -2049, 2712, -3595, 4760, -6308, 8354, -11069, 14661, -19424, 25729, -34086, 45152, ...

MCS1673313 : A₀ = 0; A₁ = 0; A₂ = 1; A_N = A_N-2 - A_N-3 - 1 (score: 5)

2, -5, 6, 3, -30, 45, 90, -495, 270, 3915, -10530, -22005, 170370, -54675, -2275830, 5371785, 25669710, -142659765, -176735250, 3064006035, -2593307070, -59157512595, 175367780730, ...

MCS863244 : A₀ = 1; A₁ = 2; A_K+1 = - 2 A_K - K A_K-1 (score: 5)

2, 5, 6, 9, 16, 19, 26, 41, 48, 63, 94, 109, 140, 203, 234, 297, 424, 487, 614, 869, 996, 1251, 1762, 2017, 2528, 3551, 4062, 5085, 7132, 8155, 10202, 14297, 16344, 20439, 28630, 32725, 40916, ...

MCS397393 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = 2 A_K-2 + K (score: 5)

2, -5, 6, -12, 17, -30, 46, -77, 122, -200, 321, -522, 842, -1365, 2206, -3572, 5777, -9350, 15126, -24477, 39602, -64080, 103681, -167762, 271442, -439205, 710646, -1149852, 1860497, -3010350, ...

MCS3436 : A₀ = 0; A₁ = 1; A_N = - A_N-1 + A_N-2 - 1 (score: 4)

2, 5, 6, 13, 10, 29, 6, 69, -38, 197, -250, 669, -1142, 2509, -4762, 9813, -19302, 38965, -77530, 155501, -310518, 621565, -1242554, 2485733, -4970790, 9942309, -19883834, 39768509, -79536118, ...

MCS7768 : A₀ = 0; A_K+1 = - 2 A_K + K² (score: 4)

2, -5, 6, -21, 26, -77, 118, -285, 506, -1093, 2086, -4293, 8442, -17053, 33910, -68045, 135834, -271957, 543590, -1087541, 2174682, -4349805, 8699126, -17398781, 34796986, -69594597, 139188518, ...

MCS248601 : A₀ = -1; A_K+1 = - 2 A_K - K² (score: 5)

2, 5, 7, 7, 6, 6, 8, 11, 13, 13, 12, 12, 14, 17, 19, 19, 18, 18, 20, 23, 25, 25, 24, 24, 26, 29, 31, 31, 30, 30, 32, 35, 37, 37, 36, 36, 38, 41, 43, 43, 42, 42, 44, 47, 49, 49, 48, 48, 50, 53, 55, ...

MCS3482817 (alias MCS13782038, MCS14062342) : A₀ = 0; A₁ = 0; A_K+1 = A_K - A_K-1 + K + 1 (score: 5)

2, 5, 7, 7, 8, 11, 13, 13, 14, 17, 19, 19, 20, 23, 25, 25, 26, 29, 31, 31, 32, 35, 37, 37, 38, 41, 43, 43, 44, 47, 49, 49, 50, 53, 55, 55, 56, 59, 61, 61, 62, 65, 67, 67, 68, 71, 73, 73, 74, 77, ...

MCS1719046 : A₀ = 1; A₁ = 1; A_K+1 = - A_K-1 + 3 K (score: 5)

2, -5, -7, -10, -5, -5, -4, -11, -13, -16, -11, -11, -10, -17, -19, -22, -17, -17, -16, -23, -25, -28, -23, -23, -22, -29, -31, -34, -29, -29, -28, -35, -37, -40, -35, -35, -34, -41, -43, -46, ...

MCS6381958 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - A_K-2 - 2 K (score: 5)

2, 5, 7, 10, 15, 19, 24, 31, 37, 44, 53, 61, 70, 81, 91, 102, 115, 127, 140, 155, 169, 184, 201, 217, 234, 253, 271, 290, 311, 331, 352, 375, 397, 420, 445, 469, 494, 521, 547, 574, 603, 631, 660, ...

MCS3186950 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K-2 + 2 K (score: 5)

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, 359, 379, 398, 419, 439, 461, 482, 505, 527, ...

MCS6956045 : A₀ = -1; A₁ = -1; A_K+1 = A_K-1 + K + 1 (score: 5)

2, 5, 7, 11, 18, 25, 31, 39, 50, 61, 71, 83, 98, 113, 127, 143, 162, 181, 199, 219, 242, 265, 287, 311, 338, 365, 391, 419, 450, 481, 511, 543, 578, 613, 647, 683, 722, 761, 799, 839, 882, 925, ...

MCS1710349 : A₀ = -1; A₁ = -1; A_K+1 = - A_K-1 + K² (score: 5)

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, ...

MCS3547 (alias MCS7083, MCS126593, MCS253186)

A_K = 3 K - 1 (score: 4)

2, -5, 8, -11, 14, -17, 20, -23, 26, -29, 32, -35, 38, -41, 44, -47, 50, -53, 56, -59, 62, -65, 68, -71, 74, -77, 80, -83, 86, -89, 92, -95, 98, -101, 104, -107, 110, -113, 116, -119, 122, -125, ...

MCS863424 : A₀ = 1; A₁ = 2; A_N = - 2 A_N-1 - A_N-2 (score: 4)

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

2, 5, 8, 12, 18, 25, 32, 40, 50, 61, 72, 84, 98, 113, 128, 144, 162, 181, 200, 220, 242, 265, 288, 312, 338, 365, 392, 420, 450, 481, 512, 544, 578, 613, 648, 684, 722, 761, 800, 840, 882, 925, ...

MCS869153 : A₀ = 0; A₁ = 0; A_K+1 = - A_K-1 + K² + 1 (score: 5)

2, 5, 8, 13, 18, 25, 32, 41, 50, 61, 72, 85, 98, 113, 128, 145, 162, 181, 200, 221, 242, 265, 288, 313, 338, 365, 392, 421, 450, 481, 512, 545, 578, 613, 648, 685, 722, 761, 800, 841, 882, 925, ...

MCS1674 (alias MCS31336, MCS501448) : A₀ = 0; A₁ = 1; A_K+1 = A_K-1 + 2 K (score: 4)

Pairwise Sums of Repeated Squares (A0982)

2, 5, 8, 15, 22, 37, 52, 83, 114, 177, 240, 367, 494, 749, 1004, 1515, 2026, 3049, 4072, 6119, 8166, 12261, 16356, 24547, 32738, 49121, 65504, 98271, 131038, 196573, 262108, 393179, 524250, ...

MCS428353 (alias MCS13586, MCS1755457) : A₀ = 0; A₁ = 0; A_K+1 = 2 A_K-1 + K (score: 4)

2, -5, 8, -19, 34, -73, 140, -287, 566, -1141, 2272, -4555, 9098, -18209, 36404, -72823, 145630, -291277, 582536, -1165091, 2330162, -4660345, 9320668, -18641359, 37282694, -74565413, 149130800, ...

MCS248673 (alias MCS501168, MCS2021058) : A₀ = -1; A_K+1 = - 2 A_K - K (score: 4)

2, 5, 9, 12, 13, 11, 7, 3, 2, 6, 15, 26, 34, 34, 24, 7, -9, -14, -1, 29, 65, 89, 84, 44, -19, -76, -92, -44, 62, 185, 261, 232, 81, -145, -341, -385, -202, 178, 603, 846, 710, 150, -652, -1317, ...

MCS6439309 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = A_K - A_K-2 + K (score: 5)

2, 5, 9, 12, 13, 13, 14, 17, 21, 24, 25, 25, 26, 29, 33, 36, 37, 37, 38, 41, 45, 48, 49, 49, 50, 53, 57, 60, 61, 61, 62, 65, 69, 72, 73, 73, 74, 77, 81, 84, 85, 85, 86, 89, 93, 96, 97, 97, 98, ...

MCS6892294 : A₀ = 1; A₁ = 1; A_K+1 = A_K - A_K-1 + 2 K (score: 5)

2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170, 189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527, 560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, ...

MCS1972 (alias MCS3924, MCS62017, MCS250433)

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

2, 5, 9, 15, 25, 40, 62, 95, 144, 216, 322, 478, 707, 1043, 1536, 2259, 3319, 4873, 7151, 10490, 15384, 22557, 33070, 48478, 71060, 104156, 152661, 223749, 327934, 480625, 704405, 1032371, ...

MCS6439174 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K + A_K-2 + K (score: 5)

2, 5, 9, 16, 27, 43, 67, 103, 156, 234, 349, 518, 766, 1130, 1664, 2447, 3595, 5278, 7745, 11361, 16661, 24429, 35814, 52500, 76955, 112796, 165324, 242308, 355134, 520489, 762829, 1117996, ...

MCS6439181 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = A_K + A_K-2 + K (score: 5)

2, 5, 9, 16, 27, 45, 74, 121, 197, 320, 519, 841, 1362, 2205, 3569, 5776, 9347, 15125, 24474, 39601, 64077, 103680, 167759, 271441, 439202, 710645, 1149849, 1860496, 3010347, 4870845, 7881194, ...

MCS1747072 : A₀ = 1; A₁ = 2; A_N = A_N-1 + A_N-2 + 2 (score: 5)

2, -5, 9, -19, 37, -75, 149, -299, 597, -1195, 2389, -4779, 9557, -19115, 38229, -76459, 152917, -305835, 611669, -1223339, 2446677, -4893355, 9786709, -19573419, 39146837, -78293675, 156587349, ...

MCS505218 : A₀ = 2; A_N = - 2 A_N-1 - 1 (score: 4)

2, -5, 9, -20, 45, -99, 218, -481, 1061, -2340, 5161, -11383, 25106, -55373, 122129, -269364, 594101, -1310331, 2890026, -6374153, 14058637, -31007300, 68388753, -150836143, 332679586, -733747925, ...

MCS6472070 : A₀ = 1; A₁ = 1; A₂ = 2; A_N = - 2 A_N-1 - A_N-3 (score: 5)

2, -5, 9, -31, 62, -249, 557, -2491, 6126, -29893, 79637, -418503, 1194554, -6696049, 20307417, -120528883, 385840922, -2410577661, 8102659361, -53032708543, 186361165302, ...

MCS54816 : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 + A_K-1 - 1 (score: 5)

2, 5, 10, 15, 20, 27, 36, 45, 54, 65, 78, 91, 104, 119, 136, 153, 170, 189, 210, 231, 252, 275, 300, 325, 350, 377, 406, 435, 464, 495, 528, 561, 594, 629, 666, 703, 740, 779, 820, 861, 902, 945, ...

MCS13388 : A₀ = 0; A₁ = 1; A_K+1 = - A_K-1 + K² + K (score: 5)

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, 1522, ...

MCS1768 (alias MCS250448) : A_K = K² + 1 (score: 3)

Squares plus one (A2522)

2, -5, -10, -18, -20, -26, -31, -44, -55, -69, -77, -89, -100, -119, -136, -156, -170, -188, -205, -230, -253, -279, -299, -323, -346, -377, -406, -438, -464, -494, -523, -560, -595, -633, -665, ...

MCS1576326 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - A_K-2 - K² (score: 5)

2, 5, 10, 18, 30, 46, 67, 94, 127, 167, 215, 271, 336, 411, 496, 592, 700, 820, 953, 1100, 1261, 1437, 1629, 1837, 2062, 2305, 2566, 2846, 3146, 3466, 3807, 4170, 4555, 4963, 5395, 5851, 6332, ...

MCS1575174 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = A_K-2 + K² (score: 5)

2, 5, 10, 19, 34, 59, 100, 167, 276, 453, 740, 1205, 1958, 3177, 5150, 8343, 13510, 21871, 35400, 57291, 92712, 150025, 242760, 392809, 635594, 1028429, 1664050, 2692507, 4356586, 7049123, ...

MCS3364 (alias MCS3482752) : A₀ = 0; A₁ = 1; A_K+1 = A_K + A_K-1 + K (score: 4)

2, 5, 10, 19, 36, 69, 134, 263, 520, 1033, 2058, 4107, 8204, 16397, 32782, 65551, 131088, 262161, 524306, 1048595, 2097172, 4194325, 8388630, 16777239, 33554456, 67108889, 134217754, 268435483, ...

MCS15701 (alias MCS1002178) : A₀ = 0; A_K+1 = 2 A_K - K + 2 (score: 5)

2, -5, 10, -19, 40, -77, 158, -311, 628, -1249, 2506, -5003, 10016, -20021, 40054, -80095, 160204, -320393, 640802, -1281587, 2563192, -5126365, 10252750, -20505479, 41010980, -82021937, ...

MCS2020994 : A₀ = 2; A_K+1 = - 2 A_K + K - 1 (score: 5)

2, 5, 10, 21, 42, 85, 170, 341, 682, 1365, 2730, 5461, 10922, 21845, 43690, 87381, 174762, 349525, 699050, 1398101, 2796202, 5592405, 11184810, 22369621, 44739242, 89478485, 178956970, 357913941, ...

MCS13602 (alias MCS1741120, MCS1741121) : A₀ = 0; A₁ = 1; A_N = A_N-1 + 2 A_N-2 + 1 (score: 5)

2, 5, 10, 25, 56, 157, 400, 1265, 3610, 12661, 39722, 151945, 516400, 2127245, 7746016, 34035937, 131682290, 612646885, 2501963530, 12252937721, 52541234152, 269564629885, ...

MCS54336 : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 + K + 1 (score: 5)

2, 5, 10, 25, 56, 157, 400, 1265, 3610, 12661, 39722, 151945, 516400, 2127245, 7746016, 34035937, 131682290, 612646885, 2501963530, 12252937721, 52541234152, 269564629885, ...

MCS856841 : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 - A_K-1 + K (score: 5)

2, 5, 11, 21, 36, 57, 85, 121, 166, 221, 287, 365, 456, 561, 681, 817, 970, 1141, 1331, 1541, 1772, 2025, 2301, 2601, 2926, 3277, 3655, 4061, 4496, 4961, 5457, 5985, 6546, 7141, 7771, 8437, 9140, ...

MCS854150 (alias MCS6902534) : A₀ = 1; A₁ = 1; A_K+1 = A_K-1 + K² (score: 4)

2, 5, 11, 21, 38, 66, 112, 187, 309, 507, 828, 1348, 2190, 3553, 5759, 9329, 15106, 24454, 39580, 64055, 103657, 167735, 271416, 439176, 710618, 1149821, 1860467, 3010317, 4870814, 7881162, ...

MCS1722625 (alias MCS3482753) : A₀ = -1; A₁ = 0; A_K+1 = A_K + A_K-1 + K (score: 5)

2, 5, 11, 22, 40, 67, 105, 156, 222, 305, 407, 530, 676, 847, 1045, 1272, 1530, 1821, 2147, 2510, 2912, 3355, 3841, 4372, 4950, 5577, 6255, 6986, 7772, 8615, 9517, 10480, 11506, 12597, 13755, ...

MCS15696 : A₀ = 0; A_K+1 = A_K + K² + 2 (score: 5)

2, 5, 11, 22, 41, 73, 126, 213, 355, 586, 961, 1569, 2554, 4149, 6731, 10910, 17673, 28617, 46326, 74981, 121347, 196370, 317761, 514177, 831986, 1346213, 2178251, 3524518, 5702825, 9227401, ...

MCS1723008 : A₀ = 1; A₁ = 2; A_K+1 = A_K + A_K-1 + 2 K (score: 5)

2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, 3145727, 6291455, 12582911, 25165823, 50331647, 100663295, 201326591, 402653183, ...

MCS250498 : A₀ = 2; A_N = 2 A_N-1 + 1 (score: 4)

2, 5, 11, 24, 50, 103, 209, 422, 848, 1701, 3407, 6820, 13646, 27299, 54605, 109218, 218444, 436897, 873803, 1747616, 3495242, 6990495, 13981001, 27962014, 55924040, 111848093, 223696199, ...

MCS1722688 : A₀ = 1; A₁ = 2; A_K+1 = A_K + 2 A_K-1 + K (score: 5)

2, 5, 11, 24, 53, 117, 258, 569, 1255, 2768, 6105, 13465, 29698, 65501, 144467, 318632, 702765, 1549997, 3418626, 7540017, 16630031, 36678688, 80897393, 178424817, 393528322, 867954037, ...

MCS403489 (alias MCS3227910) : A₀ = 0; A₁ = 1; A₂ = 1; A_N = 2 A_N-1 + A_N-3 (score: 5)

2, 5, 11, 26, 59, 137, 314, 725, 1667, 3842, 8843, 20369, 46898, 108005, 248699, 572714, 1318811, 3036953, 6993386, 16104245, 37084403, 85397138, 196650347, 452841761, 1042792802, 2401318085, ...

MCS430528 : A₀ = 1; A₁ = 2; A_N = A_N-1 + 3 A_N-2 (score: 5)

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

2, -5, -11, 29, 76, -233, -685, 2329, 7534, -27949, -97943, 391285, 1469144, -6260561, -24975449, 112690097, 474533530, -2253801941, -9965204131, 49583642701, 229199695012, ...

MCS876597 : A₀ = 0; A₁ = -1; A_K+1 = - K A_K-1 - 1 (score: 5)

2, -5, -11, 29, 76, -233, -685, 2329, 7534, -27949, -97943, 391285, 1469144, -6260561, -24975449, 112690097, 474533530, -2253801941, -9965204131, 49583642701, 229199695012, ...

MCS877069 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K-1 + A_K-1 - 1 (score: 5)

2, -5, -12, 8, 28, -33, -94, 88, 270, -277, -824, 816, 2456, -2465, -7386, 7376, 22138, -22149, -66436, 66424, 199284, -199297, -597878, 597864, 1793606, -1793621, -5380848, 5380832, 16142512, ...

MCS1718209 : A₀ = 0; A₁ = 0; A_K+1 = - 3 A_K-1 - K (score: 5)

2, 5, 12, 19, 30, 41, 56, 71, 90, 109, 132, 155, 182, 209, 240, 271, 306, 341, 380, 419, 462, 505, 552, 599, 650, 701, 756, 811, 870, 929, 992, 1055, 1122, 1189, 1260, 1331, 1406, 1481, 1560, ...

MCS31586 : A₀ = 0; A_K+1 = - A_K + 2 K² - 1 (score: 5)

2, 5, 12, 22, 38, 59, 88, 124, 170, 225, 292, 370, 462, 567, 688, 824, 978, 1149, 1340, 1550, 1782, 2035, 2312, 2612, 2938, 3289, 3668, 4074, 4510, 4975, 5472, 6000, 6562, 7157, 7788, 8454, 9158, ...

MCS868897 : A₀ = 0; A₁ = 0; A_K+1 = A_K-1 + K² + 1 (score: 5)

2, 5, 12, 23, 36, 49, 62, 77, 96, 119, 144, 169, 194, 221, 252, 287, 324, 361, 398, 437, 480, 527, 576, 625, 674, 725, 780, 839, 900, 961, 1022, 1085, 1152, 1223, 1296, 1369, 1442, 1517, 1596, ...

MCS13452 : A₀ = 0; A₁ = 1; A_K+1 = A_K - A_K-1 + K² (score: 5)

2, 5, 12, 25, 46, 77, 120, 177, 250, 341, 452, 585, 742, 925, 1136, 1377, 1650, 1957, 2300, 2681, 3102, 3565, 4072, 4625, 5226, 5877, 6580, 7337, 8150, 9021, 9952, 10945, 12002, 13125, 14316, ...

MCS31308 (alias MCS500872) : A₀ = 0; A_K+1 = A_K + K² - K + 1 (score: 5)

2, 5, 12, 27, 58, 121, 248, 503, 1014, 2037, 4084, 8179, 16370, 32753, 65520, 131055, 262126, 524269, 1048556, 2097131, 4194282, 8388585, 16777192, 33554407, 67108838, 134217701, 268435428, ...

MCS62112 (alias MCS252576, MCS1002114) : A₀ = 1; A_K+1 = 2 A_K + K (score: 3)

2^N-N (A0325)

2, -5, 12, -29, 70, -169, 408, -985, 2378, -5741, 13860, -33461, 80782, -195025, 470832, -1136689, 2744210, -6625109, 15994428, -38613965, 93222358, -225058681, 543339720, -1311738121, 3166815962, ...

MCS1726721 (alias MCS3453445) : A₀ = -1; A₁ = 0; A_N = - 2 A_N-1 + A_N-2 (score: 5)

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

2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109, 15994428, 38613965, 93222358, 225058681, 543339720, 1311738121, 3166815962, 7645370045, ...

MCS1684 (alias MCS431232, MCS6899734) : A₀ = 0; A₁ = 1; A_N = 2 A_N-1 + A_N-2 (score: 4)

Pell Numbers (A0129)

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

2, 5, 12, 33, 94, 293, 952, 3297, 11866, 44837, 175364, 713409, 2993142, 12980869, 57878000, 265571905, 1249497906, 6029792197, 29770252412, 150366096353, 775541397006, ...

MCS54400 : A₀ = 0; A₁ = 1; A_K+1 = A_K + K A_K-1 + 1 (score: 5)

2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229, 1346269, 3524578, 9227465, 24157817, 63245986, 165580141, 433494437, 1134903170, 2971215073, 7778742049, 20365011074, ...

MCS433344 (alias MCS1733382) : A₀ = 1; A₁ = 2; A_N = 3 A_N-1 - A_N-2 (score: 5)

Odd-numbered Fibonacci numbers (A1519)

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

2, -5, 13, -47, 222, -1285, 8773, -68899, 611318, -6044281, 65875773, -784464995, 10132169162, -141065903273, ...

MCS865120 : A₀ = 1; A₁ = 2; A_K+1 = - K A_K - A_K - A_K-1 (score: 5)

2, 5, 14, 33, 66, 117, 190, 289, 418, 581, 782, 1025, 1314, 1653, 2046, 2497, 3010, 3589, 4238, 4961, 5762, 6645, 7614, 8673, 9826, 11077, 12430, 13889, 15458, 17141, 18942, 20865, 22914, 25093, ...

MCS250388 : A₀ = 1; A_K+1 = A_K + 2 K² + 1 (score: 5)

2, 5, 14, 37, 90, 205, 446, 941, 1946, 3973, 8046, 16213, 32570, 65309, 130814, 261853, 523962, 1048213, 2096750, 4193861, 8388122, 16776685, 33553854, 67108237, 134217050, 268434725, 536870126, ...

MCS62088 : A₀ = 1; A_K+1 = 2 A_K + K² (score: 4)

2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162, 2391485, 7174454, 21523361, 64570082, 193710245, 581130734, 1743392201, 5230176602, 15690529805, 47071589414, 141214768241, ...

MCS63200 (alias MCS252802) : A₀ = 1; A_N = 3 A_N-1 - 1 (score: 4)

2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355, 11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197, 199037675054, ...

MCS431112 : A₀ = 1; A₁ = 2; A_K+1 = 2 A_K + K A_K-1 (score: 5)

2, 5, 14, 47, 194, 977, 5870, 41099, 328802, 2959229, 29592302, 325515335, 3906184034, 50780392457, 710925494414, ...

MCS7844 (alias MCS251024) : A₀ = 0; A_K+1 = K A_K + K + 2 (score: 5)

2, 5, 14, 47, 194, 977, 5870, 41099, 328802, 2959229, 29592302, 325515335, 3906184034, 50780392457, 710925494414, ...

MCS15668 (alias MCS501392) : A₀ = 0; A_K+1 = K A_K - A_K + K + 1 (score: 5)

2, 5, 14, 47, 194, 977, 5870, 41099, 328802, 2959229, 29592302, 325515335, 3906184034, 50780392457, 710925494414, ...

MCS15540 : A₀ = 0; A_K+1 = K A_K - 2 A_K + K (score: 5)

2, -5, 14, -58, 295, -1784, 12546, -100663, 907751, -9090056, 100091279, -1202003099, 15635130343, -218991916081, ...

MCS1579398 : A₀ = 1; A₁ = 1; A₂ = 2; A_K+1 = - K A_K - A_K-2 (score: 5)

2, -5, 16, -47, 142, -425, 1276, -3827, 11482, -34445, 103336, -310007, 930022, -2790065, 8370196, -25110587, 75331762, -225995285, 677985856, -2033957567, 6101872702, -18305618105, 54916854316, ...

MCS1003394 : A₀ = 2; A_N = - 3 A_N-1 + 1 (score: 5)

2, 5, 16, 63, 304, 1767, 12072, 94817, 841290, 8318093, 90657744, 1079574847, 13943815280, 194133839087, ...

MCS6694 : A₀ = 0; A₁ = 1; A_K+1 = K A_K - A_K-1 + K (score: 5)

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

MCS976 (alias MCS3916, MCS31248, MCS62497, MCS125328)

A₀ = 0; A_K+1 = K A_K + 1 (score: 3)

Distinct Ordered Subsets of Set with N Elements (A0522)

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