Minimally Complex Sequences  


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6, 9, 52, 95, 630, 1337, 10088, 24075, 201770, 529661, 4842492, 13771199, 135589790, 413135985, 4338873296, 14046623507, 156199438674, 533771693285, ...

MCS53506 : A0 = 0; A1 = 1; AK+1 = 2 K AK-1 + K (score: 5)

6, -2, 31, -57, 220, -596, 1869, -5507, 16642, -49782, 149515, -448349, 1345272, -4035560, 12106969, -36320583, 108962110, -326885930, 980658231, -2941974209, 8825923156, -26477768892, ...

MCS15608 : A0 = 0; AK+1 = - 3 AK + K2 (score: 5)

6, -3, -28, 45, 150, -511, -840, 5949, 3290, -74679, 31908, 1013597, -1492218, -14725335, 40093040, 224962989, -986730750, -3512529031, 24233874780, 53041763901, -610420883842, -662581449783, ...

MCS109953 : A0 = 0; A1 = 1; AK+1 = - AK - K AK-1 - 1 (score: 5)

6, -4, -4, 16, -24, 16, 16, -64, 96, -64, -64, 256, -384, 256, 256, -1024, 1536, -1024, -1024, 4096, -6144, 4096, 4096, -16384, 24576, -16384, -16384, 65536, -98304, 65536, 65536, -262144, 393216, ...

MCS13814534 : A0 = 1; A1 = 1; AN = - 2 AN-1 - 2 AN-2 (score: 5)

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

6, -4, 26, -20, 90, -108, 314, -500, 1162, -2124, 4490, -8692, 17722, -35052, 70554, -140596, 281770, -562892, 1126506, -2252212, 4505306, -9009644, 18020346, -36039540, 72080330, -144159308, ...

MCS248596 : A0 = 1; AK+1 = - 2 AK + 2 K2 (score: 5)

6, -6, 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, ...

MCS249744 : A0 = 1; AK+1 = K AK - 3 AK (score: 5)

6, -6, 24, -28, 86, -130, 316, -560, 1210, -2310, 4752, -9348, 18878, -37546, 75332, -150392, 301090, -601838, 1204056, -2407692, 4815846, -9631186, 19262924, -38525248, 77051146, -154101590, ...

MCS497288 : A0 = 1; AK+1 = - 2 AK + K2 + K (score: 5)

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

MCS864310 : A0 = 1; A1 = 1; AK+1 = - AK - K AK-1 (score: 4)

6, -8, 22, -36, 82, -152, 318, -620, 1258, -2496, 5014, -10004, 20034, -40040, 80110, -160188, 320410, -640784, 1281606, -2563172, 5126386, -10252728, 20505502, -41010956, 82021962, -164043872, ...

MCS248656 : A0 = 1; AK+1 = - 2 AK + 2 K (score: 4)

6, -9, 9, 0, -27, 81, -162, 243, -243, 0, 729, -2187, 4374, -6561, 6561, 0, -19683, 59049, -118098, 177147, -177147, 0, 531441, -1594323, 3188646, -4782969, 4782969, 0, -14348907, 43046721, ...

MCS108495 : A0 = 0; A1 = 1; AN = - 3 AN-1 - 3 AN-2 (score: 7)

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

6, -9, -4, 21, -14, -29, 56, 1, -114, 111, 116, -339, 106, 571, -784, -359, 1926, -1209, -2644, 5061, 226, -10349, 9896, 10801, -30594, 8991, 52196, -70179, -34214, 174571, -106144, -242999, ...

MCS14076678 : A0 = 1; A1 = 1; AN = - AN-1 - 2 AN-2 - 1 (score: 5)

6, -9, 11, -14, 16, -19, 21, -24, 26, -29, 31, -34, 36, -39, 41, -44, 46, -49, 51, -54, 56, -59, 61, -64, 66, -69, 71, -74, 76, -79, 81, -84, 86, -89, 91, -94, 96, -99, 101, -104, 106, -109, 111, ...

MCS14070534 : A0 = 1; A1 = 1; AN = - 2 AN-1 - AN-2 - 1 (score: 5)

6, -9, 26, -37, 98, -161, 370, -677, 1434, -2769, 5658, -11173, 22514, -44833, 89890, -179525, 359338, -718353, 1437066, -2873733, 5747906, -11495329, 22991186, -45981797, 91964218, -183927761, ...

MCS505224 : A0 = 1; AK+1 = - 2 AK + K2 - 1 (score: 5)

6, 11, 14, 19, 28, 37, 44, 53, 66, 79, 90, 103, 120, 137, 152, 169, 190, 211, 230, 251, 276, 301, 324, 349, 378, 407, 434, 463, 496, 529, 560, 593, 630, 667, 702, 739, 780, 821, 860, 901, 946, ...

MCS13420 : A0 = 0; A1 = 1; AK+1 = - AK-1 + K2 - K (score: 5)

6, 11, 28, 47, 92, 143, 248, 367, 596, 855, 1336, 1879, 2868, 3983, 5992, 8255, 12308, 16871, 25016, 34183, 50516, 68895, 101608, 138415, 203892, 277559, 408568, 555959, 818036, 1112879, 1637096, ...

MCS6676 : A0 = 0; A1 = 1; AK+1 = 2 AK-1 + K2 (score: 5)

6, 11, 41, 96, 301, 781, 2286, 6191, 17621, 48576, 136681, 379561, 1062966, 2960771, 8275601, 23079456, 64457461, 179854741, 502142046, 1401415751, 3912125981, 10919204736, 30479834641, ...

MCS6727 : A0 = 0; A1 = 1; AN = AN-1 + 5 AN-2 (score: 7)

Horadam sequence Wn(0, 1; 5, 1), Lucas sequence Un(1, -5)

6, 12, 40, 85, 276, 644, 2272, 5877, 22820, 64768, 273984, 842153, 3835972, 12632520, 61375808, 214753129, 1104764868, 4080309812, 22095297760, 85686506493, 486096551204, ...

MCS13320 : A0 = 0; A1 = 1; AK+1 = K AK-1 + K2 (score: 5)

6, 13, 22, 33, 46, 61, 78, 97, 118, 141, 166, 193, 222, 253, 286, 321, 358, 397, 438, 481, 526, 573, 622, 673, 726, 781, 838, 897, 958, 1021, 1086, 1153, 1222, 1293, 1366, 1441, 1518, 1597, 1678, ...

MCS14204 : AK = K2 - 3 (score: 5)

6, 14, 25, 39, 56, 76, 99, 125, 154, 186, 221, 259, 300, 344, 391, 441, 494, 550, 609, 671, 736, 804, 875, 949, 1026, 1106, 1189, 1275, 1364, 1456, 1551, 1649, 1750, 1854, 1961, 2071, 2184, 2300, ...

MCS7891 : A0 = 0; AK+1 = AK + 3 K - 1 (score: 5)

6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1770, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 2850, ...

MCS7066 : AK = 2 K2 - K (score: 4)

6, 15, 34, 57, 102, 139, 234, 261, 478, 375, 978, 241, 2262, -1149, 6394, -7875, 21582, -36305, 80610, -151959, 314566, -616965, 1247754, -2479883, 4977342, -9935001, 19891954, -39759519, ...

MCS15536 : A0 = 0; AK+1 = - 2 AK + K3 (score: 5)

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, 2176, 2310, 2448, 2590, 2736, 2886, ...

MCS28338 : AK = 2 K2 - 2 (score: 5)

6, 16, -20, -132, 28, 1216, 936, -12440, -23672, 138048, 469456, -1601264, -9112560, 18108928, 182135008, -161934624, -3804634784, -404007680, 83297957568, 92590134208, ...

MCS107585 (alias MCS3442742) : A0 = 0; A1 = 1; AK+1 = AK - K AK-1 + AK-1 (score: 5)

6, 16, -20, -132, 28, 1216, 936, -12440, -23672, 138048, 469456, -1601264, -9112560, 18108928, 182135008, -161934624, -3804634784, -404007680, 83297957568, 92590134208, ...

MCS860214 : A0 = 1; A1 = 1; AK+1 = AK - K AK-1 (score: 4)

6, 17, 36, 65, 106, 161, 232, 321, 430, 561, 716, 897, 1106, 1345, 1616, 1921, 2262, 2641, 3060, 3521, 4026, 4577, 5176, 5825, 6526, 7281, 8092, 8961, 9890, 10881, 11936, 13057, 14246, 15505, ...

MCS504968 : A0 = 1; AK+1 = AK + K2 + K - 1 (score: 5)

6, 18, 42, 78, 132, 204, 300, 420, 570, 750, 966, 1218, 1512, 1848, 2232, 2664, 3150, 3690, 4290, 4950, 5676, 6468, 7332, 8268, 9282, 10374, 11550, 12810, 14160, 15600, 17136, 18768, 20502, 22338, ...

MCS15576 : A0 = 0; AK+1 = - AK + K3 - K (score: 5)

6, 20, 43, 77, 124, 186, 265, 363, 482, 624, 791, 985, 1208, 1462, 1749, 2071, 2430, 2828, 3267, 3749, 4276, 4850, 5473, 6147, 6874, 7656, 8495, 9393, 10352, 11374, 12461, 13615, 14838, 16132, ...

MCS31440 : A0 = 0; AK+1 = AK + K2 - 2 (score: 5)

6, 20, 43, 81, 134, 208, 303, 425, 574, 756, 971, 1225, 1518, 1856, 2239, 2673, 3158, 3700, 4299, 4961, 5686, 6480, 7343, 8281, 9294, 10388, 11563, 12825, 14174, 15616, 17151, 18785, 20518, 22356, ...

MCS15792 : A0 = 0; AK+1 = - AK + K3 - 1 (score: 5)

6, 20, 50, 112, 238, 492, 1002, 2024, 4070, 8164, 16354, 32736, 65502, 131036, 262106, 524248, 1048534, 2097108, 4194258, 8388560, 16777166, 33554380, 67108810, 134217672, 268435398, 536870852, ...

MCS248481 : A0 = -1; AK+1 = 2 AK + 2 K (score: 5)

6, 21, 58, 141, 318, 685, 1434, 2949, 5998, 12117, 24378, 48925, 98046, 196317, 392890, 786069, 1572462, 3145285, 6290970, 12582381, 25165246, 50331021, 100662618, 201325861, 402652398, 805305525, ...

MCS3880 : A0 = 0; AK+1 = 2 AK + K2 (score: 4)

6, 24, 60, 120, 210, 336, 504, 720, 990, 1320, 1716, 2184, 2730, 3360, 4080, 4896, 5814, 6840, 7980, 9240, 10626, 12144, 13800, 15600, 17550, 19656, 21924, 24360, 26970, 29760, 32736, 35904, ...

MCS3532 : AK = K3 - K (score: 4)

6, 25, 62, 123, 214, 341, 510, 727, 998, 1329, 1726, 2195, 2742, 3373, 4094, 4911, 5830, 6857, 7998, 9259, 10646, 12165, 13822, 15623, 17574, 19681, 21950, 24387, 26998, 29789, 32766, 35935, ...

MCS14168 : AK = K3 - 2 (score: 5)

6, 27, 78, 191, 430, 923, 1926, 3951, 8022, 16187, 32542, 65279, 130782, 261819, 523926, 1048175, 2096710, 4193819, 8388078, 16776639, 33553806, 67108187, 134216998, 268434671, 536870070, ...

MCS15784 : A0 = 0; AK+1 = 2 AK + K2 - 1 (score: 5)

6, 27, 112, 453, 1818, 7279, 29124, 116505, 466030, 1864131, 7456536, 29826157, 119304642, 477218583, 1908874348, 7635497409, 30541989654, 122167958635, 488671834560, ...

MCS3886 : A0 = 0; AK+1 = 4 AK + K (score: 5)

6, 27, 124, 645, 3906, 27391, 219192, 1972809, 19728190, 217010211, 2604122676, 33853594957, 473950329594, ...

MCS1924 (alias MCS30792, MCS61585) : A0 = 0; AK+1 = K AK + K2 (score: 4)

6, 30, 90, 210, 420, 756, 1260, 1980, 2970, 4290, 6006, 8190, 10920, 14280, 18360, 23256, 29070, 35910, 43890, 53130, 63756, 75900, 89700, 105300, 122850, 142506, 164430, 188790, 215760, 245520, ...

MCS15512 : A0 = 0; AK+1 = AK + K3 - K (score: 5)

6, 32, 95, 219, 434, 776, 1287, 2015, 3014, 4344, 6071, 8267, 11010, 14384, 18479, 23391, 29222, 36080, 44079, 53339, 63986, 76152, 89975, 105599, 123174, 142856, 164807, 189195, 216194, 245984, ...

MCS15776 : A0 = 0; AK+1 = AK + K3 - 1 (score: 5)

6, 33, 202, 1419, 11358, 102229, 1022298, 11245287, 134943454, 1754264913, 24559708794, 368395631923, ...

MCS7764 : A0 = 0; AK+1 = K AK + 2 AK + K (score: 5)

6, 33, 202, 1419, 11358, 102229, 1022298, 11245287, 134943454, 1754264913, 24559708794, 368395631923, ...

MCS504976 : A0 = 1; AK+1 = K AK + AK + K - 1 (score: 5)

6, 39, 316, 3165, 37986, 531811, 8508984, 153161721, 3063234430, 67391157471, ...

MCS3858 (alias MCS61736, MCS123473) : A0 = 0; AK+1 = 2 K AK + K (score: 4)

6, 42, 156, 420, 930, 1806, 3192, 5256, 8190, 12210, 17556, 24492, 33306, 44310, 57840, 74256, 93942, 117306, 144780, 176820, 213906, 256542, 305256, 360600, 423150, 493506, 572292, 660156, ...

MCS496267 : A0 = 0; AK+1 = AK + 4 K3 + 2 K (score: 9)

A puzzle sequence from Terry Stickel (possibly same as A82986)

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, -193870043, ...

MCS505248 : A0 = 1; AK+1 = - 2 AK + K - 1 (score: 4)

6, -11, 41, -96, 301, -781, 2286, -6191, 17621, -48576, 136681, -379561, 1062966, -2960771, 8275601, -23079456, 64457461, -179854741, 502142046, -1401415751, 3912125981, -10919204736, 30479834641, ...

MCS6759 : A0 = 0; A1 = 1; AN = - AN-1 + 5 AN-2 (score: 7)

Horadam sequence Wn(0, 1; 5, -1), Lucas sequence Un(-1, -5)

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

MCS869901 : A0 = 0; A1 = 0; AK+1 = - K AK-1 - K + 1 (score: 5)

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

MCS858893 : A0 = 0; A1 = 0; AK+1 = - K AK-1 - AK-1 - K (score: 5)

6, -14, 26, -54, 106, -214, 426, -854, 1706, -3414, 6826, -13654, 27306, -54614, 109226, -218454, 436906, -873814, 1747626, -3495254, 6990506, -13981014, 27962026, -55924054, 111848106, ...

MCS503136 : A0 = 1; AN = - 2 AN-1 - 2 (score: 4)

6, -14, 47, -135, 412, -1228, 3693, -11069, 33218, -99642, 298939, -896803, 2690424, -8071256, 24213785, -72641337, 217924030, -653772070, 1961316231, -5883948671, 17651846036, -52955538084, ...

MCS3902 (alias MCS15678) : A0 = 0; AK+1 = - 3 AK + K (score: 4)

6, -16, 37, -91, 218, -528, 1273, -3075, 7422, -17920, 43261, -104443, 252146, -608736, 1469617, -3547971, 8565558, -20679088, 49923733, -120526555, 290976842, -702480240, 1695937321, -4094354883, ...

MCS13740 : A0 = 0; A1 = 1; AN = - 2 AN-1 + AN-2 - 1 (score: 5)

6, -16, 44, -120, 328, -896, 2448, -6688, 18272, -49920, 136384, -372608, 1017984, -2781184, 7598336, -20759040, 56714752, -154947584, 423324672, -1156544512, 3159738368, -8632565760, 23584608256, ...

MCS13490 : A0 = 0; A1 = 1; AN = - 2 AN-1 + 2 AN-2 (score: 5)

(Not in OEIS)

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

6, -17, 43, -135, 388, -1349, 4269, -16187, 55498, -226617, 832471, -3625871, 14152008, -65265677, 268888153, -1305313539, 5646651214, -28716897857, 129872977923, -689205548567, ...

MCS1736781 : A0 = -1; A1 = -1; AK+1 = K AK-1 + 1 (score: 5)

6, -18, 48, -156, 492, -1740, 6168, -23568, 91416, -374232, 1562640, -6801888, 30241488, -139071696, 653176992, -3156467520, 15566830368, -78696180768, 405599618496, ...

MCS864293 : A0 = 0; A1 = -1; AK+1 = - AK + K AK-1 (score: 5)

6, -18, 60, -210, 780, -3030, 12300, -51870, 226740, -1024050, 4768980, -22850610, 112466940, -567693030, 2934857100, -15520495710, 83868419220, -462626256930, ...

MCS53952 : A0 = 0; A1 = 1; AK+1 = - 2 AK + K AK-1 (score: 5)

6, -19, 55, -168, 500, -1505, 4509, -13534, 40594, -121791, 365363, -1096100, 3288288, -9864877, 29594617, -88783866, 266351582, -799054763, 2397164271, -7191492832, 21574478476, -64723435449, ...

MCS1003440 : A0 = 1; AK+1 = - 3 AK - K + 1 (score: 5)

6, -23, 113, -672, 4681, -37335, 335343, -3348749, 36798904, -441251505, 5732920816, -80224092520, ...

MCS394817 : A0 = 0; A1 = 0; A2 = 1; AK+1 = - K AK + AK-2 (score: 5)

6, -24, 22, -55, 67, -133, 188, -334, 508, -857, 1349, -2223, 3554, -5796, 9330, -15147, 24455, -39625, 64056, -103706, 167736, -271469, 439177, -710675, 1149822, -1860528, 3010318, -4870879, ...

MCS1731841 : A0 = -1; A1 = 0; AK+1 = - AK + AK-1 - K (score: 5)

6, -24, 120, -720, 5040, -40320, 362880, -3628800, 39916800, -479001600, 6227020800, -87178291200, ...

MCS62257 : A0 = -1; AK+1 = - K AK - AK (score: 4)

6, -24, 120, -720, 5040, -40320, 362880, -3628800, 39916800, -479001600, 6227020800, -87178291200, ...

MCS124312 : A0 = 1; AK+1 = - K AK - 2 AK (score: 4)

6, -25, 127, -768, 5401, -43335, 390783, -3913231, 43088876, -517457295, 6730858066, -94275101800, ...

MCS394849 : A0 = 0; A1 = 0; A2 = 1; AK+1 = - K AK - AK-2 (score: 5)

6, -27, 36, -93, 162, -351, 672, -1377, 2718, -5475, 10908, -21861, 43674, -87399, 174744, -349545, 699030, -1398123, 2796180, -5592429, 11184786, -22369647, 44739216, -89478513, 178956942, ...

MCS31087 : A0 = 0; AK+1 = - 2 AK - 3 K (score: 5)

6, -27, 132, -795, 5562, -44499, 400488, -4004883, 44053710, -528644523, 6872378796, -96213303147, ...

MCS15857 (alias MCS253720) : A0 = 0; AK+1 = - K AK - 3 (score: 5)

7, 5, -15, -8, 53, 33, -149, -88, 459, 277, -1363, -816, 4105, 2465, -12297, -7376, 36911, 22149, -110711, -66424, 332157, 199297, -996445, -597864, 2989363, 1793621, -8968059, -5380832, 26904209, ...

MCS13391 : A0 = 0; A1 = 1; AK+1 = - 3 AK-1 + K (score: 5)

7, 5, -33, 13, 119, -171, -305, 989, 231, -4187, 3263, 13485, -26537, -27403, 133551, -23939, -510265, 606021, 1435039, -3859123, -1881033, 17317525, -9793393, -59476707, 98650279, 139256549, ...

MCS27031 : A0 = 0; A1 = 1; AN = - AN-1 - 4 AN-2 (score: 6)

(Not in OEIS)

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

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

MCS878605 : A0 = 0; A1 = 0; AK+1 = AK - K AK-1 - 1 (score: 5)

7, 7, -20, -20, 61, 61, -182, -182, 547, 547, -1640, -1640, 4921, 4921, -14762, -14762, 44287, 44287, -132860, -132860, 398581, 398581, -1195742, -1195742, 3587227, 3587227, -10761680, -10761680, ...

MCS13583 (alias MCS1738689, MCS6954758) : A0 = 0; A1 = 1; AN = - 3 AN-2 + 1 (score: 5)

7, 9, 1, -15, -25, -11, 29, 65, 47, -47, -159, -159, 47, 365, 477, 65, -777, -1319, -607, 1489, 3415, 2533, -2371, -8319, -8481, 2209, 19009, 25281, 4063, -40227, -69571, -33407, 76391, 179369, ...

MCS25740854 : A0 = 1; A1 = 1; A2 = 1; AN = AN-1 - AN-2 - AN-3 (score: 5)

7, 9, 71, 109, 995, 1745, 17911, 34901, 394043, 837625, 10245119, 23453501, 307353571, 750512033, 10450021415, 27018433189, 397100813771, ...

MCS434197 : A0 = 0; A1 = 0; AK+1 = 2 K AK-1 + 1 (score: 5)

7, 9, -37, -57, 303, 521, -3021, -5721, 36263, 74385, -507669, -1115761, 8122719, 18967953, -146208925, -360391089, 2924178519, 7568212889, -64331927397, -174068896425, ...

MCS3427382 : A0 = 1; A1 = 1; AK+1 = - K AK-1 - AK-1 + K (score: 5)

7, -3, 9, -17, 15, -35, 49, -65, 119, -163, 249, -401, 575, -899, 1377, -2049, 3175, -4803, 7273, -11153, 16879, -25699, 39185, -59457, 90583, -137827, 209497, -318993, 485151, -737987, 1123137, ...

MCS790705 (alias MCS25302582) : A0 = 0; A1 = 1; A2 = 1; AN = AN-2 - 2 AN-3 (score: 5)

7, -7, -33, 69, 155, -715, -689, 7829, -261, -93699, 97079, 1214693, -2670893, -16764211, 62169375, 239586405, -1420804549, -3370923571, 33207819079, 40952499461, -804732338301, -178127648787, ...

MCS3463222 : A0 = 1; A1 = 1; AK+1 = - AK - K AK-1 - K (score: 5)

7, -8, 25, -38, 91, -164, 349, -674, 1375, -2720, 5473, -10910, 21859, -43676, 87397, -174746, 349543, -699032, 1398121, -2796182, 5592427, -11184788, 22369645, -44739218, 89478511, -178956944, ...

MCS248688 : A0 = 1; AK+1 = - 2 AK + 3 K (score: 5)

7, 10, -5, -26, -17, 34, 67, -2, -137, -134, 139, 406, 127, -686, -941, 430, 2311, 1450, -3173, -6074, 271, 12418, 11875, -12962, -36713, -10790, 62635, 84214, -41057, -209486, -127373, 291598, ...

MCS14060294 : A0 = 1; A1 = 1; AN = AN-1 - 2 AN-2 - 1 (score: 5)

7, 11, 13, 19, 29, 37, 43, 53, 67, 79, 89, 103, 121, 137, 151, 169, 191, 211, 229, 251, 277, 301, 323, 349, 379, 407, 433, 463, 497, 529, 559, 593, 631, 667, 701, 739, 781, 821, 859, 901, 947, ...

MCS3435654 : A0 = 1; A1 = 1; AK+1 = - AK-1 + K2 - K (score: 5)

7, 11, 21, 29, 43, 55, 73, 89, 111, 131, 157, 181, 211, 239, 273, 305, 343, 379, 421, 461, 507, 551, 601, 649, 703, 755, 813, 869, 931, 991, 1057, 1121, 1191, 1259, 1333, 1405, 1483, 1559, 1641, ...

MCS124457 : A0 = -1; AK+1 = - AK + 2 K2 (score: 5)

7, 14, -37, -86, 257, 686, -2315, -6862, 25463, 82342, -331021, -1152790, 4965313, 18444638, -84410323, -332003486, 1603796135, 6640069718, -33679718837, -146081533798, 774633533249, ...

MCS3498038 : A0 = 1; A1 = 1; AK+1 = - K AK-1 - 2 (score: 5)

7, 17, 25, 33, 47, 65, 81, 97, 119, 145, 169, 193, 223, 257, 289, 321, 359, 401, 441, 481, 527, 577, 625, 673, 727, 785, 841, 897, 959, 1025, 1089, 1153, 1223, 1297, 1369, 1441, 1519, 1601, 1681, ...

MCS1710406 : A0 = 1; A1 = 1; AK+1 = - AK-1 + 2 K2 (score: 5)

7, 17, 31, 49, 71, 97, 127, 161, 199, 241, 287, 337, 391, 449, 511, 577, 647, 721, 799, 881, 967, 1057, 1151, 1249, 1351, 1457, 1567, 1681, 1799, 1921, 2047, 2177, 2311, 2449, 2591, 2737, 2887, ...

MCS7090 : AK = 2 K2 - 1 (score: 4)

7, 19, 39, 69, 111, 167, 239, 329, 439, 571, 727, 909, 1119, 1359, 1631, 1937, 2279, 2659, 3079, 3541, 4047, 4599, 5199, 5849, 6551, 7307, 8119, 8989, 9919, 10911, 11967, 13089, 14279, 15539, ...

MCS248081 (alias MCS248209) : A0 = -1; AK+1 = AK + K2 + K (score: 5)

7, 20, 44, 81, 135, 208, 304, 425, 575, 756, 972, 1225, 1519, 1856, 2240, 2673, 3159, 3700, 4300, 4961, 5687, 6480, 7344, 8281, 9295, 10388, 11564, 12825, 14175, 15616, 17152, 18785, 20519, 22356, ...

MCS3888 : A0 = 0; AK+1 = - AK + K3 (score: 4)

7, 21, 44, 78, 125, 187, 266, 364, 483, 625, 792, 986, 1209, 1463, 1750, 2072, 2431, 2829, 3268, 3750, 4277, 4851, 5474, 6148, 6875, 7657, 8496, 9394, 10353, 11375, 12462, 13616, 14839, 16133, ...

MCS503048 : A0 = 1; AK+1 = AK + K2 - 2 (score: 5)

7, 21, 51, 113, 239, 493, 1003, 2025, 4071, 8165, 16355, 32737, 65503, 131037, 262107, 524249, 1048535, 2097109, 4194259, 8388561, 16777167, 33554381, 67108811, 134217673, 268435399, 536870853, ...

MCS15786 : A0 = 0; AK+1 = 2 AK + 2 K - 1 (score: 5)

7, 22, 50, 95, 161, 252, 372, 525, 715, 946, 1222, 1547, 1925, 2360, 2856, 3417, 4047, 4750, 5530, 6391, 7337, 8372, 9500, 10725, 12051, 13482, 15022, 16675, 18445, 20336, 22352, 24497, 26775, ...

MCS31026 : A0 = 0; AK+1 = AK + 2 K2 - K (score: 5)

7, 22, -38, -161, 282, 1487, -2659, -16639, 30421, 218966, -409255, -3314911, 6329114, 56762742, -110609141, -1084821212, 2155420078, 22891854593, -46334420504, -528668075717, ...

MCS196825 : A0 = 0; A1 = 1; A2 = 1; AK+1 = - K AK-1 - AK-2 (score: 5)

7, 24, 55, 104, 175, 272, 399, 560, 759, 1000, 1287, 1624, 2015, 2464, 2975, 3552, 4199, 4920, 5719, 6600, 7567, 8624, 9775, 11024, 12375, 13832, 15399, 17080, 18879, 20800, 22847, 25024, 27335, ...

MCS31554 : A0 = 0; AK+1 = AK + 2 K2 - 1 (score: 5)

7, 25, 61, 121, 211, 337, 505, 721, 991, 1321, 1717, 2185, 2731, 3361, 4081, 4897, 5815, 6841, 7981, 9241, 10627, 12145, 13801, 15601, 17551, 19657, 21925, 24361, 26971, 29761, 32737, 35905, ...

MCS14156 : AK = K3 - K + 1 (score: 5)

7, 25, -69, -299, 967, 4785, -17405, -95699, 382911, 2296777, -9955685, -64309755, 298670551, 2057912161, -10154798733, -74084837795, 385882351855, ...

MCS3473590 : A0 = 1; A1 = 1; AK+1 = - 2 K AK-1 + 1 (score: 5)

7, 26, 57, 99, 159, 244, 353, 485, 647, 846, 1081, 1351, 1663, 2024, 2433, 2889, 3399, 3970, 4601, 5291, 6047, 6876, 7777, 8749, 9799, 10934, 12153, 13455, 14847, 16336, 17921, 19601, 21383, ...

MCS6680 : A0 = 0; A1 = 1; AK+1 = - AK-1 + K3 (score: 5)

7, 26, 63, 124, 215, 342, 511, 728, 999, 1330, 1727, 2196, 2743, 3374, 4095, 4912, 5831, 6858, 7999, 9260, 10647, 12166, 13823, 15624, 17575, 19682, 21951, 24388, 26999, 29790, 32767, 35936, ...

MCS3544 : AK = K3 - 1 (score: 4)

7, 26, -17, -200, -65, 1734, 2383, -16692, -45289, 171706, 805751, -1769840, -14661857, 15425422, 279338847, -13744172, -5600521113, -5311893502, 117899570983, 240073121528, ...

MCS109825 : A0 = 0; A1 = 1; AK+1 = AK - K AK-1 - 1 (score: 5)

7, 27, 57, 98, 159, 245, 353, 484, 647, 847, 1081, 1350, 1663, 2025, 2433, 2888, 3399, 3971, 4601, 5290, 6047, 6877, 7777, 8748, 9799, 10935, 12153, 13454, 14847, 16337, 17921, 19600, 21383, ...

MCS855110 : A0 = 1; A1 = 1; AK+1 = - AK-1 + K3 (score: 5)

7, 27, 127, 695, 4431, 32415, 268191, 2478559, 25321983, 283498943, 3452631295, 45451204735, 643222128895, ...

MCS27694341 : A0 = 0; A1 = -1; AK+1 = K AK - AK + 2 AK-1 + K (score: 8)

Simplest continuation of 7, 27, 127 (see 695)

7, 30, 106, 343, 1065, 3244, 9796, 29469, 88507, 265642, 797070, 2391379, 7174333, 21523224, 64569928, 193710073, 581130543, 1743391990, 5230176370, 15690529551, 47071589137, 141214767940, ...

MCS3896 : A0 = 0; AK+1 = 3 AK + K2 (score: 5)

7, 31, 91, 211, 421, 757, 1261, 1981, 2971, 4291, 6007, 8191, 10921, 14281, 18361, 23257, 29071, 35911, 43891, 53131, 63757, 75901, 89701, 105301, 122851, 142507, 164431, 188791, 215761, 245521, ...

MCS124100 : A0 = 1; AK+1 = AK + K3 - K (score: 5)

7, 33, 96, 220, 435, 777, 1288, 2016, 3015, 4345, 6072, 8268, 11011, 14385, 18480, 23392, 29223, 36081, 44080, 53340, 63987, 76153, 89976, 105600, 123175, 142857, 164808, 189196, 216195, 245985, ...

MCS126212 : A0 = 1; AK+1 = AK + K3 - 1 (score: 5)

7, 37, 201, 1231, 8653, 69273, 623521, 6235291, 68588301, 823059733, 10699776673, 149796873591, ...

MCS7748 : A0 = 0; AK+1 = K AK + AK + K2 (score: 5)

7, 52, 472, 5197, 67567, 1013512, 17229712, 327364537, 6874655287, 158117071612, ...

MCS15506 : A0 = 0; AK+1 = 2 K AK + AK + K (score: 5)

7, -11, 27, -47, 103, -195, 403, -791, 1599, -3179, 6379, -12735, 25495, -50963, 101955, -203879, 407791, -815547, 1631131, -3262223, 6524487, -13048931, 26097907, -52195767, 104391583, ...

MCS1010512 : A0 = 1; AK+1 = - 2 AK + 2 K - 1 (score: 5)

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

MCS2012576 : A0 = 1; AK+1 = - 2 AK + K - 2 (score: 5)

7, -15, 31, -63, 127, -255, 511, -1023, 2047, -4095, 8191, -16383, 32767, -65535, 131071, -262143, 524287, -1048575, 2097151, -4194303, 8388607, -16777215, 33554431, -67108863, 134217727, ...

MCS54245 : A0 = 0; A1 = 1; AN = - 3 AN-1 - 2 AN-2 (score: 6)

(Not in OEIS)

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

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

MCS1015136 : A0 = 1; AN = - 2 AN-1 - 3 (score: 5)

7, -17, 41, -99, 239, -577, 1393, -3363, 8119, -19601, 47321, -114243, 275807, -665857, 1607521, -3880899, 9369319, -22619537, 54608393, -131836323, 318281039, -768398401, 1855077841, -4478554083, ...

MCS6906893 : A0 = -1; A1 = -1; AN = - 2 AN-1 + AN-2 (score: 5)

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

7, -20, 33, -74, 139, -288, 565, -1142, 2271, -4556, 9097, -18210, 36403, -72824, 145629, -291278, 582535, -1165092, 2330161, -4660346, 9320667, -18641360, 37282693, -74565414, 149130799, ...

MCS62893 : A0 = 0; AK+1 = - 2 AK - K - 2 (score: 5)

7, -20, 61, -182, 547, -1640, 4921, -14762, 44287, -132860, 398581, -1195742, 3587227, -10761680, 32285041, -96855122, 290565367, -871696100, 2615088301, -7845264902, 23535794707, -70607384120, ...

MCS3919 (alias MCS13491, MCS250848) : A0 = 0; AN = - 3 AN-1 + 1 (score: 4)

(1 - (-3)n)/4 (A14983)

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

7, -23, 76, -251, 829, -2738, 9043, -29867, 98644, -325799, 1076041, -3553922, 11737807, -38767343, 128039836, -422886851, 1396700389, -4612988018, 15235664443, -50319981347, 166195608484, ...

MCS6943238 : A0 = 1; A1 = 1; AN = - 3 AN-1 + AN-2 (score: 5)

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

7, -25, 69, -215, 635, -1917, 5737, -17227, 51663, -155009, 465005, -1395039, 4185091, -12555301, 37665873, -112997651, 338992919, -1016978793, 3050936341, -9152809063, 27458427147, -82375281485, ...

MCS999088 : A0 = 1; AK+1 = - 3 AK - 2 K (score: 5)

7, -26, 37, -92, 163, -350, 673, -1376, 2719, -5474, 10909, -21860, 43675, -87398, 174745, -349544, 699031, -1398122, 2796181, -5592428, 11184787, -22369646, 44739217, -89478512, 178956943, ...

MCS994800 : A0 = 1; AK+1 = - 2 AK - 3 K (score: 5)

7, -26, 133, -794, 5563, -44498, 400489, -4004882, 44053711, -528644522, 6872378797, -96213303146, ...

MCS31433 (alias MCS502936) : A0 = 0; AK+1 = - K AK + K - 2 (score: 5)

7, -26, 133, -794, 5563, -44498, 400489, -4004882, 44053711, -528644522, 6872378797, -96213303146, ...

MCS497304 : A0 = 1; AK+1 = - K AK - 2 AK + K (score: 5)

7, -27, 133, -791, 5510, -43947, 394732, -3941810, 43315963, -519396824, 6748216902, -94431720665, ...

MCS197409 : A0 = 0; A1 = 1; A2 = 1; AK+1 = - K AK + AK-2 (score: 5)

7, -28, 26, -64, 79, -155, 221, -390, 596, -1002, 1581, -2601, 4163, -6784, 10926, -17732, 28635, -46391, 75001, -121418, 196392, -317838, 514201, -832069, 1346239, -2178340, 3524546, -5702920, ...

MCS14080518 : A0 = 1; A1 = 1; AK+1 = - AK + AK-1 - K - 1 (score: 5)

7, -30, 157, -972, 6961, -56660, 516901, -5225670, 57999271, -701216922, 9173819257, -129134686520, ...

MCS13449 : A0 = 0; A1 = 1; AK+1 = - K AK + AK + AK-1 (score: 5)

7, -30, 157, -972, 6961, -56660, 516901, -5225670, 57999271, -701216922, 9173819257, -129134686520, ...

MCS3417622 : A0 = 1; A1 = 0; AK+1 = - K AK + AK-1 (score: 5)

7, -30, 157, -972, 6961, -56660, 516901, -5225670, 57999271, -701216922, 9173819257, -129134686520, ...

MCS13513 : A0 = 0; A1 = 1; AK+1 = - K AK - AK + AK-1 (score: 5)

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

MCS249265 : A0 = -1; AK+1 = - K AK - AK - K (score: 5)

7, -31, 191, -1331, 10655, -95887, 958879, -10547659, 126571919, -1645434935, 23036089103, -345541336531, ...

MCS7785 : A0 = 0; AK+1 = - K AK - AK + K (score: 4)

7, -33, 191, -1304, 10241, -90865, 898409, -9791634, 116601199, -1506023953, 20967734143, -313009988192, ...

MCS3341 : A0 = 0; A1 = 1; AK+1 = - K AK - AK-1 (score: 4)

7, -40, 313, -3090, 36767, -511648, 8149601, -146181170, 2915473799, -63994242408, ...

MCS13365 : A0 = 0; A1 = 1; AK+1 = - 2 K AK - AK-1 (score: 5)

7, -44, 349, -3494, 41923, -586928, 9390841, -169035146, 3380702911, -74375464052, ...

MCS31285 (alias MCS500568) : A0 = 0; AK+1 = - 2 K AK - K + 1 (score: 5)

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

MCS31533 (alias MCS504536) : A0 = 0; AK+1 = - K AK - 2 K - 1 (score: 5)

7, -47, 83, -419, 1075, -4855, 15595, -69011, 256139, -1153295, 4739227, -22038667, 97866283, -472523639, 2234116715, -11212065875, 55894400155, -291347783551, ...

MCS3463206 : A0 = 1; A1 = 1; AK+1 = - AK + K AK-1 - K (score: 5)

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

MCS6657 : A0 = 0; A1 = 1; AK+1 = - K AK-1 (score: 3)


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Quick Index:
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