Minimally Complex Sequences  


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

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

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

MCS12864 (alias MCS1646656, MCS1646657, MCS6586637)

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

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

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

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

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

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

Fibonacci numbers (A0045)

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

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

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

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

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

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

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

Horadam sequence Wn(2, 3; -2, 3), Lucas sequence Vn(3, 2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

MCS428289 (alias MCS869505, MCS3499137, MCS3510789)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2, 3, 7, 16, 35, 77, 170, 375, 827, 1824, 4023, 8873, 19570, 43163, 95199, 209968, 463099, 1021397, 2252762, 4968623, 10958643, 24170048, 53308719, 117576081, 259322210, 571953139, 1261482359, ...

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

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

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

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

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

Bisection of Lucas numbers (A5248)

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

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

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

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

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

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

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

2, 3, 8, 11, 18, 23, 32, 39, 50, 59, 72, 83, 98, 111, 128, 143, 162, 179, 200, 219, 242, 263, 288, 311, 338, 363, 392, 419, 450, 479, 512, 543, 578, 611, 648, 683, 722, 759, 800, 839, 882, 923, ...

MCS31592 (alias MCS1714693) : A0 = 0; AK+1 = - AK + K2 + K - 1 (score: 5)

2, 3, 8, 11, 22, 29, 52, 67, 114, 145, 240, 303, 494, 621, 1004, 1259, 2026, 2537, 4072, 5095, 8166, 10213, 16356, 20451, 32738, 40929, 65504, 81887, 131038, 163805, 262108, 327643, 524250, ...

MCS1739073 : A0 = 0; A1 = 0; AK+1 = 2 AK-1 + K + 1 (score: 5)

2, 3, 8, 14, 22, 28, 35, 42, 53, 65, 79, 91, 104, 117, 134, 152, 172, 190, 209, 228, 251, 275, 301, 325, 350, 375, 404, 434, 466, 496, 527, 558, 593, 629, 667, 703, 740, 777, 818, 860, 904, 946, ...

MCS1575302 : A0 = 1; A1 = 1; A2 = 2; AK+1 = - AK-2 + K2 (score: 5)

2, 3, 8, 15, 28, 45, 70, 101, 142, 191, 252, 323, 408, 505, 618, 745, 890, 1051, 1232, 1431, 1652, 1893, 2158, 2445, 2758, 3095, 3460, 3851, 4272, 4721, 5202, 5713, 6258, 6835, 7448, 8095, 8780, ...

MCS856608 : A0 = 1; A1 = 2; AK+1 = AK-1 + K2 + K (score: 5)

2, 3, 8, 15, 32, 55, 100, 159, 264, 399, 628, 919, 1400, 2007, 2996, 4239, 6248, 8767, 12820, 17895, 26040, 36231, 52564, 72991, 105704, 146607, 212084, 293943, 424952, 588727, 850804, 1178415, ...

MCS427296 : A0 = 1; A1 = 2; AK+1 = 2 AK-1 + K2 (score: 5)

2, 3, 8, 15, 40, 85, 252, 609, 2032, 5499, 20340, 60511, 244104, 786669, 3417484, 11800065, 54679776, 200601139, 984236004, 3811421679, 19684720120, 80039855301, 433063842684, ...

MCS428552 : A0 = 1; A1 = 2; AK+1 = K AK-1 + 2 K (score: 5)

2, 3, 8, 15, 44, 95, 314, 767, 2834, 7679, 31184, 92159, 405404, 1290239, 6081074, 20643839, 103378274, 371589119, 1964187224, 7431782399, 41247931724, 163499212799, 948702429674, ...

MCS856584 : A0 = 1; A1 = 2; AK+1 = K AK-1 + AK-1 + K (score: 5)

2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 2027025, 10321920, 34459425, 185794560, 654729075, 3715891200, 13749310575, 81749606400, 316234143225, ...

MCS213030 : A0 = 1; A1 = 1; AK+1 = K AK-1 (score: 3)

Semifactorials or ''double'' factorials (A6882)

2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 2027025, 10321920, 34459425, 185794560, 654729075, 3715891200, 13749310575, 81749606400, 316234143225, ...

MCS854054 : A0 = 1; A1 = 1; AK+1 = K AK-1 + AK-1 (score: 4)

Semifactorials or ''double'' factorials (A6882)

2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 2027025, 10321920, 34459425, 185794560, 654729075, 3715891200, 13749310575, 81749606400, 316234143225, ...

MCS427272 : A0 = 1; A1 = 2; AK+1 = K AK-1 + 2 AK-1 (score: 5)

Semifactorials or ''double'' factorials (A6882)

2, 3, 8, 19, 46, 111, 268, 647, 1562, 3771, 9104, 21979, 53062, 128103, 309268, 746639, 1802546, 4351731, 10506008, 25363747, 61233502, 147830751, 356895004, 861620759, 2080136522, 5021893803, ...

MCS1724930 : A0 = 2; A1 = 3; AN = 2 AN-1 + AN-2 (score: 5)

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

2, 3, 8, 27, 116, 607, 3758, 26913, 219062, 1998471, 20203772, 224239963, 2711083328, 35468323227, 499267608506, ...

MCS213568 : A0 = 1; A1 = 2; AK+1 = K AK + AK-1 (score: 4)

2, 3, 8, 30, 147, 874, 6088, 48557, 436139, 4355302, 47859765, 573881041, 7456098231, 104337515469, ...

MCS1577350 : A0 = 1; A1 = 1; A2 = 2; AK+1 = K AK - AK-2 (score: 5)

2, 3, 9, 16, 60, 119, 524, 1130, 5645, 13036, 72255, 176859, 1070789, 2757489, 18026554, 48564013, 339747037, 953253706, 7086123764, 20631834495, 162027592866, 488077904116, ...

MCS6298166 : A0 = 1; A1 = 1; A2 = 1; AK+1 = K AK-1 - AK-2 (score: 5)

2, 3, 9, 17, 62, 135, 557, 1349, 6126, 16187, 79637, 226617, 1194554, 3625871, 20307417, 65265677, 385840922, 1305313539, 8102659361, 28716897857, 186361165302, 689205548567, ...

MCS3508262 : A0 = 1; A1 = 1; AK+1 = K AK-1 + AK-1 - 1 (score: 5)

2, 3, 9, 19, 73, 191, 877, 2675, 14033, 48151, 280661, 1059323, 6735865, 27542399, 188604221, 826271971, 6035335073, 28093247015, 217272062629, ...

MCS434196 : A0 = 1; A1 = 2; AK+1 = 2 K AK-1 + 1 (score: 5)

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

MCS1663040 : A0 = 1; A1 = 2; A2 = 3; AN = AN-3 - 2 (score: 5)

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

MCS208928 : A0 = 0; A1 = 2; A2 = 3; AN = AN-3 - 1 (score: 5)

2, 3, -1, 1, 10, 15, 15, 21, 34, 43, 47, 57, 74, 87, 95, 109, 130, 147, 159, 177, 202, 223, 239, 261, 290, 315, 335, 361, 394, 423, 447, 477, 514, 547, 575, 609, 650, 687, 719, 757, 802, 843, 879, ...

MCS855170 : A0 = 2; A1 = 3; AK+1 = - AK-1 + K2 (score: 5)

2, 3, -1, 2, 8, -3, -3, 20, -2, -25, 43, 22, -92, 65, 137, -248, -6, 523, -489, -534, 1536, -443, -2603, 3516, 1718, -8721, 5315, 12158, -22756, -1527, 47073, -43984, -50126, 138131, -37841, ...

MCS3461825 : A0 = 0; A1 = 0; AK+1 = - AK - 2 AK-1 + K (score: 5)

2, 3, -1, 4, 0, 0, 5, -4, 5, 1, -4, 10, -8, 5, 6, -13, 19, -12, 0, 20, -31, 32, -11, -19, 52, -62, 44, 9, -70, 115, -105, 36, 80, -184, 221, -140, -43, 265, -404, 362, -96, -307, 670, -765, 459, ...

MCS1650752 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-1 + AN-3 + 1 (score: 5)

2, 3, -1, 4, -5, 9, -14, 23, -37, 60, -97, 157, -254, 411, -665, 1076, -1741, 2817, -4558, 7375, -11933, 19308, -31241, 50549, -81790, 132339, -214129, 346468, -560597, 907065, -1467662, 2374727, ...

MCS864770 : A0 = 2; A1 = 3; AN = - AN-1 + AN-2 (score: 4)

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

2, 3, -1, 5, 1, -3, 13, -11, 5, 21, -43, 53, -11, -75, 181, -203, 53, 309, -715, 821, -203, -1227, 2869, -3275, 821, 4917, -11467, 13109, -3275, -19659, 45877, -52427, 13109, 78645, -183499, ...

MCS811168 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-1 + 2 AN-3 (score: 5)

2, 3, -1, 5, -16, 69, -361, 2235, -16006, 130283, -1188553, 12015813, -133362496, 1612365765, -21094117441, 296930009939, ...

MCS854402 : A0 = 2; A1 = 3; AK+1 = - K AK + AK-1 (score: 5)

2, 3, -1, 7, -10, 38, -88, 316, -932, 3460, -11848, 46448, -176776, 734152, -3032240, 13310368, -58793968, 271759856, -1271257312, 6162934720, -30316823648, 153575518048, -790228814656, ...

MCS864290 : A0 = 2; A1 = 3; AK+1 = - AK + K AK-1 (score: 5)

2, 3, -1, -1, 4, 0, -5, 4, 5, -9, -1, 14, -8, -15, 22, 7, -37, 15, 44, -52, -29, 96, -23, -125, 119, 102, -244, 17, 346, -261, -329, 607, 68, -936, 539, 1004, -1475, -465, 2479, -1010, -2944, ...

MCS396352 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-2 + AN-3 (score: 4)

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

MCS856834 : A0 = 2; A1 = 3; AK+1 = - AK-1 + K (score: 4)

2, 3, -1, -1, -1, -6, -7, -8, -14, -16, -18, -25, -28, -31, -39, -43, -47, -56, -61, -66, -76, -82, -88, -99, -106, -113, -125, -133, -141, -154, -163, -172, -186, -196, -206, -221, -232, -243, ...

MCS399424 : A0 = 1; A1 = 2; A2 = 3; AK+1 = AK-2 - K (score: 4)

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

MCS869122 (alias MCS6953005) : A0 = 2; A1 = 3; AN = - AN-2 + 1 (score: 4)

2, 3, -1, -2, 2, 8, 6, -3, -6, 6, 19, 11, -13, -17, 16, 45, 17, -44, -44, 46, 108, 19, -132, -104, 137, 261, -7, -371, -226, 407, 627, -150, -1002, -444, 1186, 1481, -706, -2630, -737, 3375, 3407, ...

MCS1592416 : A0 = 1; A1 = 2; A2 = 3; AK+1 = - AK-1 - AK-2 + K (score: 5)

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

MCS98400 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-3 (score: 3)

2, 3, -1, -2, -8, -6, -12, -5, -14, -2, -19, 1, -29, 7, -44, 21, -67, 48, -106, 96, -174, 181, -292, 332, -497, 599, -855, 1069, -1482, 1895, -2581, 3346, -4508, 5894, -7888, 10367, -13818, 18218, ...

MCS1599584 : A0 = 1; A1 = 2; A2 = 3; AK+1 = AK-1 - AK-2 - K (score: 5)

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

MCS208944 : A0 = 0; A1 = 2; A2 = 3; AN = - AN-3 - 1 (score: 5)

2, 3, -1, -3, -5, 3, 7, 11, -5, -13, -21, 11, 27, 43, -21, -53, -85, 43, 107, 171, -85, -213, -341, 171, 427, 683, -341, -853, -1365, 683, 1707, 2731, -1365, -3413, -5461, 2731, 6827, 10923, ...

MCS1638752 : A0 = 1; A1 = 2; A2 = 3; AN = - 2 AN-3 + 1 (score: 5)

2, 3, -1, -4, 6, 20, -25, -114, 182, 920, -1629, -9190, 17930, 110292, -233077, -1544074, 3496170, 24705200, -59434873, -444693582, 1129262606, 8893871660, -23714514705, -195665176498, ...

MCS856114 : A0 = 2; A1 = 3; AK+1 = - K AK-1 + K (score: 5)

2, 3, -1, -5, 4, 21, -19, -125, 134, 1001, -1205, -10009, 13256, 120109, -172327, -1681525, 2584906, 26904401, -43943401, -484279217, 834924620, 9685584341, -17533417019, -213082855501, ...

MCS868402 : A0 = 2; A1 = 3; AK+1 = - K AK-1 + 1 (score: 5)

2, 3, -1, -5, -2, 6, 7, -4, -13, -3, 17, 16, -14, -33, -2, 47, 35, -45, -82, 10, 127, 72, -137, -199, 65, 336, 134, -401, -470, 267, 871, 203, -1138, -1074, 935, 2212, 139, -3147, -2351, 3008, ...

MCS25368758 : A0 = 1; A1 = 1; A2 = 0; AN = - AN-2 - AN-3 (score: 5)

2, 3, -1, -7, -5, 9, 19, 1, -37, -39, 35, 113, 43, -183, -269, 97, 635, 441, -829, -1711, -53, 3369, 3475, -3263, -10213, -3687, 16739, 24113, -9365, -57591, -38861, 76321, 154043, 1401, -306685, ...

MCS3443458 : A0 = 2; A1 = 3; AN = AN-1 - 2 AN-2 (score: 5)

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

2, 3, -2, 3, -2, 9, -6, 15, -16, 31, -36, 63, -82, 131, -180, 277, -392, 589, -848, 1259, -1828, 2697, -3934, 5785, -8458, 12417, -18176, 26661, -39050, 57255, -83886, 122967, -180190, 264109, ...

MCS1626208 : A0 = 1; A1 = 2; A2 = 3; AK+1 = - AK - AK-2 + K (score: 5)

2, 3, -2, 3, -8, 7, -20, 21, -48, 61, -118, 169, -298, 455, -766, 1207, -1988, 3179, -5184, 8345, -13548, 21873, -35442, 57293, -92758, 150027, -242810, 392811, -635648, 1028431, -1664108, ...

MCS3463682 : A0 = 2; A1 = 3; AK+1 = - AK + AK-1 - K (score: 5)

2, 3, -2, 3, -8, 13, -24, 45, -82, 151, -278, 511, -940, 1729, -3180, 5849, -10758, 19787, -36394, 66939, -123120, 226453, -416512, 766085, -1409050, 2591647, -4766782, 8767479, -16125908, ...

MCS1624160 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-1 + AN-2 - AN-3 (score: 5)

2, 3, -2, 4, -1, -1, 5, -6, 5, 0, -6, 11, -11, 5, 6, -17, 22, -16, -1, 23, -39, 38, -15, -24, 62, -77, 53, 9, -86, 139, -130, 44, 95, -225, 269, -174, -51, 320, -494, 443, -123, -371, 814, -937, ...

MCS405568 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-1 + AN-3 (score: 4)

2, 3, -2, 4, -7, 10, -18, 27, -46, 72, -119, 190, -310, 499, -810, 1308, -2119, 3426, -5546, 8971, -14518, 23488, -38007, 61494, -99502, 160995, -260498, 421492, -681991, 1103482, -1785474, ...

MCS3518978 : A0 = 2; A1 = 3; AN = - AN-1 + AN-2 - 1 (score: 5)

2, 3, -2, -1, 5, -1, -6, 6, 5, -12, 1, 17, -13, -16, 30, 3, -46, 27, 49, -73, -22, 122, -51, -144, 173, 93, -317, 80, 410, -397, -330, 807, -67, -1137, 874, 1070, -2011, -196, 3081, -1815, -3277, ...

MCS198176 : A0 = 0; A1 = 2; A2 = 3; AN = - AN-2 + AN-3 (score: 5)

2, 3, -2, -1, -1, -7, -7, -8, -15, -16, -18, -26, -28, -31, -40, -43, -47, -57, -61, -66, -77, -82, -88, -100, -106, -113, -126, -133, -141, -155, -163, -172, -187, -196, -206, -222, -232, -243, ...

MCS199712 : A0 = 0; A1 = 2; A2 = 3; AK+1 = AK-2 - K (score: 5)

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

MCS3511042 : A0 = 2; A1 = 3; AK+1 = - AK-1 + K - 1 (score: 5)

2, 3, -2, -2, 4, -1, -7, 4, 5, -12, -2, 16, -11, -19, 26, 7, -46, 18, 52, -65, -35, 116, -31, -152, 146, 120, -299, 25, 418, -325, -394, 742, 68, -1137, 673, 1204, -1811, -532, 3014, -1280, -3547, ...

MCS1674304 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-2 + AN-3 - 1 (score: 5)

2, 3, -2, -2, -2, -8, -9, -10, -17, -19, -21, -29, -32, -35, -44, -48, -52, -62, -67, -72, -83, -89, -95, -107, -114, -121, -134, -142, -150, -164, -173, -182, -197, -207, -217, -233, -244, -255, ...

MCS1677376 : A0 = 1; A1 = 2; A2 = 3; AK+1 = AK-2 - K - 1 (score: 5)

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

MCS213762 : A0 = 2; A1 = 3; AN = - AN-2 (score: 3)

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

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

MCS417888 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-3 - 1 (score: 4)

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

MCS3480322 : A0 = 2; A1 = 3; AK+1 = - AK-1 - K + 1 (score: 5)

2, 3, -2, -4, 0, 7, 5, -6, -11, 2, 18, 10, -19, -27, 10, 47, 18, -56, -64, 39, 121, 26, -159, -146, 134, 306, 13, -439, -318, 427, 758, -108, -1184, -649, 1293, 1834, -643, -3126, -1190, 3770, ...

MCS1641568 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-2 - AN-3 + 1 (score: 5)

2, 3, -2, -4, -6, 4, 8, 12, -8, -16, -24, 16, 32, 48, -32, -64, -96, 64, 128, 192, -128, -256, -384, 256, 512, 768, -512, -1024, -1536, 1024, 2048, 3072, -2048, -4096, -6144, 4096, 8192, 12288, ...

MCS393568 : A0 = 1; A1 = 2; A2 = 3; AN = - 2 AN-3 (score: 4)

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

MCS1644640 : A0 = 1; A1 = 2; A2 = 3; AK+1 = - AK-2 - K + 1 (score: 5)

2, 3, -2, -5, -1, 7, 6, -6, -13, 0, 19, 13, -19, -32, 6, 51, 26, -57, -77, 31, 134, 46, -165, -180, 119, 345, 61, -464, -406, 403, 870, 3, -1273, -873, 1270, 2146, -397, -3416, -1749, 3813, 5165, ...

MCS198192 : A0 = 0; A1 = 2; A2 = 3; AN = - AN-2 - AN-3 (score: 5)

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

MCS199728 : A0 = 0; A1 = 2; A2 = 3; AK+1 = - AK-2 - K (score: 5)

2, 3, -2, -6, 6, 24, -30, -144, 210, 1152, -1890, -11520, 20790, 138240, -270270, -1935360, 4054050, 30965760, -68918850, -557383680, 1309458150, 11147673600, -27498621150, -245248819200, ...

MCS213042 : A0 = 2; A1 = 3; AK+1 = - K AK-1 (score: 4)

2, 3, -2, -7, 16, 49, -104, -383, 946, 3841, -10394, -46079, 135136, 645121, -2027024, -10321919, 34459426, 185794561, -654729074, -3715891199, 13749310576, 81749606401, -316234143224, ...

MCS869389 : A0 = 0; A1 = 0; AK+1 = - K AK-1 + K + 1 (score: 5)

2, 3, -2, -9, -6, 11, 22, -1, -46, -45, 46, 135, 42, -229, -314, 143, 770, 483, -1058, -2025, 90, 4139, 3958, -4321, -12238, -3597, 20878, 28071, -13686, -69829, -42458, 97199, 182114, -12285, ...

MCS3515073 : A0 = 0; A1 = 0; AN = AN-1 - 2 AN-2 - 1 (score: 5)

2, 3, -2, -31, -126, -377, -970, -2283, -5078, -10885, -22770, -46871, -95470, -193137, -389018, -781411, -1566918, -3138749, -6283330, -12573519, -25155038, -50319337, -100649322, -201310811, ...

MCS62086 : A0 = 1; AK+1 = 2 AK - K3 (score: 5)

2, 3, -3, 1, -4, 7, -8, 12, -19, 27, -39, 58, -85, 124, -182, 267, -391, 573, -840, 1231, -1804, 2644, -3875, 5679, -8323, 12198, -17877, 26200, -38398, 56275, -82475, 120873, -177148, 259623, ...

MCS202800 : A0 = 0; A1 = 2; A2 = 3; AN = - AN-1 - AN-3 (score: 5)

2, 3, -3, 2, -4, 8, -9, 14, -21, 31, -44, 66, -96, 141, -206, 303, -443, 650, -952, 1396, -2045, 2998, -4393, 6439, -9436, 13830, -20268, 29705, -43534, 63803, -93507, 137042, -200844, 294352, ...

MCS1650784 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-1 - AN-3 + 1 (score: 5)

2, 3, -3, 4, -2, -2, 5, -8, 5, -1, -8, 12, -14, 5, 6, -21, 25, -20, -2, 26, -47, 44, -19, -29, 72, -92, 62, 9, -102, 163, -155, 52, 110, -266, 317, -208, -59, 375, -584, 524, -150, -435, 958, ...

MCS1683520 : A0 = 1; A1 = 2; A2 = 3; AN = - AN-1 + AN-3 - 1 (score: 5)

2, 3, -3, 5, -2, -1, 6, -8, 7, -1, -7, 14, -15, 8, 6, -21, 29, -23, 2, 27, -50, 52, -25, -25, 77, -102, 77, 0, -102, 179, -179, 77, 102, -281, 358, -256, -25, 383, -639, 614, -231, -408, 1022, ...

MCS202784 : A0 = 0; A1 = 2; A2 = 3; AN = - AN-1 + AN-3 (score: 5)

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

MCS877314 : A0 = 2; A1 = 3; AN = - AN-2 - 1 (score: 4)

2, 3, -3, -4, 2, -4, -12, -1, 0, -20, -11, 9, -21, -33, 16, -3, -65, 2, 44, -86, -62, 109, -46, -194, 131, 123, -351, -19, 446, -361, -495, 776, 102, -1304, 640, 1371, -1980, -768, 3313, -1251, ...

MCS1600576 : A0 = 1; A1 = 2; A2 = 3; AK+1 = - AK-1 + AK-2 - K (score: 5)

2, 3, -3, -4, 9, 5, -22, -1, 49, -20, -99, 89, 178, -277, -267, 732, 257, -1731, 218, 3719, -2167, -7220, 8053, 12273, -23326, -16493, 58925, 9660, -134343, 39605, 278346, -213553, -517087, ...

MCS1584192 : A0 = 1; A1 = 2; A2 = 3; AN = - 2 AN-2 + AN-3 (score: 5)

2, 3, -3, -4, 9, 12, -13, -18, 33, 44, -57, -78, 125, 168, -237, -322, 489, 660, -961, -1302, 1941, 2624, -3861, -5226, 7745, 10476, -15465, -20926, 30957, 41880, -61885, -83730, 123801, 167492, ...

MCS3427074 : A0 = 2; A1 = 3; AK+1 = - 2 AK-1 + K (score: 5)


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    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,...
    Sequences Beginning 2,5,... ; 2,6,... and 2,7,...
    Sequences Beginning 2,8,... ; 2,9,... ; etc.
    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.
    Sequences Beginning 4,6,... ; 4,7,... ; etc.
    Sequences Beginning 5,...
    Sequences Beginning 6,... ; 7,... ; etc.



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