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Proceed to Safety

Minimally Complex Sequences

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14, -117, 1164, -13975, 195642, -3130281, 56345048, -1126900971, 24791821350, -595003712413, ...

MCS31541 (alias MCS504664) : A₀ = 0; A_K+1 = - 2 K A_K - K - 1 (score: 5)

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

MCS26721 (alias MCS106521) : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 - A_K-1 (score: 4)

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

MCS854069 (alias MCS1708141) : A₀ = 0; A₁ = -1; A_K+1 = - K A_K-1 + A_K-1 (score: 5)

15, 9, -104, -87, 927, 974, -10110, -12615, 130456, 186720, -1944225, -3117976, 32865105, 58067793, -621319019, -1194220965, 12989631606, 26894180249, -297567305973, -658449957582, ...

MCS393649 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = - K A_K-1 - A_K-2 (score: 5)

15, -9, -104, 87, 927, -974, -10110, 12615, 130456, -186720, -1944225, 3117976, 32865105, -58067793, -621319019, 1194220965, 12989631606, -26894180249, -297567305973, 658449957582, ...

MCS393521 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = - K A_K-1 + A_K-2 (score: 5)

15, 24, -105, -192, 945, 1920, -10395, -23040, 135135, 322560, -2027025, -5160960, 34459425, 92897280, -654729075, -1857945600, 13749310575, 40874803200, -316234143225, -980995276800, ...

MCS3419190 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K-1 - 2 A_K-1 (score: 5)

15, 44, -155, -534, 2163, 8536, -38943, -170730, 856735, 4097508, -22275123, -114730238, 668253675, 3671367600, -22720624967, -132169233618, 863383748727, ...

MCS3432630 : A₀ = 1; A₁ = 1; A_K+1 = - 2 K A_K-1 - K (score: 5)

15, 53, 127, 249, 431, 685, 1023, 1457, 1999, 2661, 3455, 4393, 5487, 6749, 8191, 9825, 11663, 13717, 15999, 18521, 21295, 24333, 27647, 31249, 35151, 39365, 43903, 48777, 53999, 59581, 65535, ...

MCS14178 : A_K = 2 K³ - 1 (score: 5)

15, -56, 209, -780, 2911, -10864, 40545, -151316, 564719, -2107560, 7865521, -29354524, 109552575, -408855776, 1525870529, -5694626340, 21252634831, -79315912984, 296011017105, ...

MCS27001 : A₀ = 0; A₁ = 1; A_N = - 4 A_N-1 - A_N-2 (score: 6)

Horadam sequence W_n(0, 1; -1, -4), Lucas sequence U_n(-4, 1)

15, -62, 245, -984, 3931, -15730, 62913, -251660, 1006631, -4026534, 16106125, -64424512, 257698035, -1030792154, 4123168601, -16492674420, 65970697663, -263882790670, ...

MCS497584 : A₀ = 1; A_K+1 = - 4 A_K - K (score: 5)

15, -63, 58, -143, 177, -346, 495, -871, 1334, -2239, 3537, -5814, 9311, -15167, 24434, -39647, 64033, -103730, 167711, -271495, 439150, -710703, 1149793, -1860558, 3010287, -4870911, 7881130, ...

MCS13851142 : A₀ = 1; A₁ = 1; A_K+1 = - A_K + A_K-1 - 2 K (score: 5)

15, -76, 455, -3186, 25487, -229384, 2293839, -25232230, 302786759, -3936227868, 55107190151, -826607852266, ...

MCS7897 : A₀ = 0; A_K+1 = - K A_K - A_K - 1 (score: 4)

15, -86, 588, -4617, 40966, -405042, 4414497, -52568921, 678981477, -9453171756, 141118594864, ...

MCS13581 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K - A_K-1 + 1 (score: 5)

15, 105, -75, -1545, -345, 27465, 34365, -569865, -1394625, 13421865, 52471365, -350184585, -2029268265, 9877007625, 82930665165, -292395624585, ...

MCS107525 : A₀ = 0; A₁ = 1; A_K+1 = A_K - 2 K A_K-1 (score: 5)

15, -105, 945, -10395, 135135, -2027025, 34459425, -654729075, 13749310575, -316234143225, ...

MCS249009 : A₀ = -1; A_K+1 = - 2 K A_K - A_K (score: 5)

15, -105, 945, -10395, 135135, -2027025, 34459425, -654729075, 13749310575, -316234143225, ...

MCS247985 : A₀ = -1; A_K+1 = - 2 K A_K + A_K (score: 5)

15, -116, 1165, -13974, 195643, -3130280, 56345049, -1126900970, 24791821351, -595003712412, ...

MCS7717 (alias MCS123480, MCS246961) : A₀ = 0; A_K+1 = - 2 K A_K + K (score: 4)

15, -306, 1799, -14904, 133407, -1335070, 14684439, -176214996, 2290792751, -32071101258, 481066515495, ...

MCS7705 (alias MCS30822) : A₀ = 0; A_K+1 = - K A_K - K³ (score: 5)

16, 0, -64, 0, 256, 0, -1024, 0, 4096, 0, -16384, 0, 65536, 0, -262144, 0, 1048576, 0, -4194304, 0, 16777216, 0, -67108864, 0, 268435456, 0, -1073741824, 0, 4294967296, 0, -17179869184, 0, ...

MCS6679 : A₀ = 0; A₁ = 1; A_N = - 4 A_N-2 (score: 5)

(Not in OEIS)

Horadam sequence W_n(0, 1; -4, 0), Lucas sequence U_n(0, 4)

16, -10, -108, 56, 848, -522, -8500, 5720, 101976, -74386, -1427692, 1115760, 22843040, -18967954, -411174756, 360391088, 8223495080, -7568212890, -180916891804, 174068896424, ...

MCS107201 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 - 2 K (score: 5)

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, -1396115, ...

MCS13455 (alias MCS6889222) : A₀ = 0; A₁ = 1; A_N = A_N-1 - 3 A_N-2 (score: 5)

Horadam sequence W_n(0, 1; -3, 1), Lucas sequence U_n(1, 3) ; Horadam sequence W_n(1, 1; -3, 1)

16, 16, -64, -64, 256, 256, -1024, -1024, 4096, 4096, -16384, -16384, 65536, 65536, -262144, -262144, 1048576, 1048576, -4194304, -4194304, 16777216, 16777216, -67108864, -67108864, 268435456, ...

MCS3419910 : A₀ = 1; A₁ = 1; A_N = - 4 A_N-2 (score: 5)

Horadam sequence W_n(1, 1; -4, 0)

16, -64, 256, -1024, 4096, -16384, 65536, -262144, 1048576, -4194304, 16777216, -67108864, 268435456, -1073741824, 4294967296, -17179869184, 68719476736, -274877906944, ...

MCS124384 : A₀ = 1; A_N = - 4 A_N-1 (score: 4)

16, -90, 528, -3710, 29664, -266994, 2669920, -29369142, 352429680, -4581585866, 64142202096, -962133031470, ...

MCS7725 (alias MCS123608, MCS247217) : A₀ = 0; A_K+1 = - K A_K - 2 K (score: 4)

17, 39, -171, -469, 2393, 7503, -43075, -150061, 947649, 3601463, -24638875, -100840965, 739166249, 3226910879, -25131652467, -116168791645, 955002793745, ...

MCS3506358 : A₀ = 1; A₁ = 1; A_K+1 = - 2 K A_K-1 - 1 (score: 5)

17, -66, 267, -1064, 4261, -17038, 68159, -272628, 1090521, -4362074, 17448307, -69793216, 279172877, -1116691494, 4466765991, -17867063948, 71468255809, -285873023218, ...

MCS497568 : A₀ = 1; A_K+1 = - 4 A_K + K (score: 5)

17, -72, 305, -1292, 5473, -23184, 98209, -416020, 1762289, -7465176, 31622993, -133957148, 567451585, -2403763488, 10182505537, -43133785636, 182717648081, -774004377960, ...

MCS13500 : A₀ = 0; A₁ = 1; A_N = - 4 A_N-1 + A_N-2 (score: 6)

(Not in OEIS)

Horadam sequence W_n(0, 1; 1, -4), Lucas sequence U_n(-4, -1)

17, -89, 529, -3709, 29665, -266993, 2669921, -29369141, 352429681, -4581585865, 64142202097, -962133031469, ...

MCS124632 : A₀ = 1; A_K+1 = - K A_K - A_K - K (score: 4)

17, -89, 529, -3709, 29665, -266993, 2669921, -29369141, 352429681, -4581585865, 64142202097, -962133031469, ...

MCS7821 (alias MCS125144, MCS250289) : A₀ = 0; A_K+1 = - K A_K - K + 1 (score: 4)

18, 28, -152, -261, 1510, 2860, -18132, -37193, 253834, 557880, -4061360, -9483977, 73104462, 180195544, -1462089260, -3784106445, 32165963698, 87034448212, -771983128776, ...

MCS858165 : A₀ = 0; A₁ = -1; A_K+1 = - K A_K-1 - K (score: 5)

18, -80, 356, -1584, 7048, -31360, 139536, -620864, 2762528, -12291840, 54692416, -243353344, 1082798208, -4817899520, 21437194496, -95384577024, 424412697088, ...

MCS54002 : A₀ = 0; A₁ = 1; A_N = - 4 A_N-1 + 2 A_N-2 (score: 7)

Horadam sequence W_n(0, 1; 2, -4), Lucas sequence U_n(-4, -2)

19, -11, -179, 311, 2195, -7171, -32339, 175759, 535699, -4753915, -9174259, 142283879, 132943891, -4686028019, 165935725, 168531072959, -174836630509, ...

MCS3457206 : A₀ = 1; A₁ = 1; A_K+1 = - A_K - 2 K A_K-1 (score: 5)

19, 29, -151, -260, 1511, 2861, -18131, -37192, 253835, 557881, -4061359, -9483976, 73104463, 180195545, -1462089259, -3784106444, 32165963699, 87034448213, -771983128775, ...

MCS869133 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K-1 - A_K-1 + 1 (score: 5)

19, 29, -151, -260, 1511, 2861, -18131, -37192, 253835, 557881, -4061359, -9483976, 73104463, 180195545, -1462089259, -3784106444, 32165963699, 87034448213, -771983128775, ...

MCS3473622 : A₀ = 1; A₁ = 0; A_K+1 = - K A_K-1 + 1 (score: 5)

19, -77, 307, -1229, 4915, -19661, 78643, -314573, 1258291, -5033165, 20132659, -80530637, 322122547, -1288490189, 5153960755, -20615843021, 82463372083, -329853488333, ...

MCS505312 : A₀ = 1; A_N = - 4 A_N-1 - 1 (score: 5)

19, -111, 641, -4523, 36135, -325279, 3252709, -35779899, 429358667, -5581662815, 78143279241, ...

MCS124524 : A₀ = 1; A_K+1 = - K A_K - A_K - K² (score: 5)

20, -20, -120, 280, 800, -3600, -5200, 48400, 19200, -696800, 408800, 10740000, -17689600, -175630400, 511732800, 3000875200, -13747264000, -52271990400, 368459062400, 886068707200, ...

MCS864309 : A₀ = 0; A₁ = -1; A_K+1 = - A_K - K A_K-1 (score: 5)

20, 20, -120, -280, 800, 3600, -5200, -48400, 19200, 696800, 408800, -10740000, -17689600, 175630400, 511732800, -3000875200, -13747264000, 52271990400, 368459062400, -886068707200, ...

MCS26881 : A₀ = 0; A₁ = 1; A_K+1 = A_K - K A_K-1 (score: 4)

20, 20, -120, -280, 800, 3600, -5200, -48400, 19200, 696800, 408800, -10740000, -17689600, 175630400, 511732800, -3000875200, -13747264000, 52271990400, 368459062400, -886068707200, ...

MCS3443766 : A₀ = 1; A₁ = 1; A_K+1 = A_K - K A_K-1 - A_K-1 (score: 5)

20, 35, -234, -483, 3752, 8703, -75030, -191455, 1800732, 4977843, -50420482, -149335275, 1613455440, 5077399367, -58084395822, -192941175927, ...

MCS107013 : A₀ = 0; A₁ = 1; A_K+1 = - 2 K A_K-1 + K (score: 5)

20, -106, 655, -4692, 38190, -348403, 3522219, -39092813, 472635974, -6183360476, 87039682637, ...

MCS877153 : A₀ = 0; A₁ = 0; A_K+1 = - K A_K + A_K-1 - 1 (score: 5)

21, 0, -231, 0, 3465, 0, -65835, 0, 1514205, 0, -40883535, 0, 1267389585, 0, -44358635475, 0, ...

MCS106757 : A₀ = 0; A₁ = 1; A_K+1 = - 2 K A_K-1 + A_K-1 (score: 5)

21, -11, -153, 81, 1369, -819, -15069, 9817, 195885, -137451, -2938289, 2199201, 49950897, -39585635, -949067061, 791712681, 19930408261, -17417679003, -458399390025, 418024296049, ...

MCS107361 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 - A_K-1 - K (score: 5)

21, 45, -231, -585, 3465, 9945, -65835, -208845, 1514205, 5221125, -40883535, -151412625, 1267389585, 4996616625, -44358635475, -184874815125, ...

MCS3420342 : A₀ = 1; A₁ = 1; A_K+1 = - 2 K A_K-1 - A_K-1 (score: 5)

24, 0, -192, 0, 1920, 0, -23040, 0, 322560, 0, -5160960, 0, 92897280, 0, -1857945600, 0, 40874803200, 0, -980995276800, 0, ...

MCS106849 : A₀ = 0; A₁ = 1; A_K+1 = - K A_K-1 - 2 A_K-1 (score: 5)

24, -93, 131, -328, 578, -1247, 2389, -4898, 9660, -19473, 38775, -77740, 155270, -310771, 621289, -1242854, 2485408, -4971141, 9941931, -19884240, 39768074, -79536583, 159072701, -318145898, ...

MCS1731905 : A₀ = 0; A₁ = 0; A_K+1 = - A_K + 2 A_K-1 - K (score: 5)

24, -115, 551, -2640, 12649, -60605, 290376, -1391275, 6665999, -31938720, 153027601, -733199285, 3512968824, -16831644835, 80645255351, -386394631920, ...

MCS27005 : A₀ = 0; A₁ = 1; A_N = - 5 A_N-1 - A_N-2 (score: 7)

Horadam sequence W_n(0, 1; -1, -5), Lucas sequence U_n(-5, 1)

24, -135, 792, -5565, 44496, -400491, 4004880, -44053713, 528644520, -6872378799, 96213303144, ...

MCS15485 (alias MCS247768) : A₀ = 0; A_K+1 = - K A_K - 3 K (score: 5)

24, -212, 2337, -30375, 455632, -7745736, 147168993, -3090548843, 71082623400, ...

MCS31141 : A₀ = 0; A_K+1 = - 2 K A_K - A_K + K (score: 5)

25, 0, -125, 0, 625, 0, -3125, 0, 15625, 0, -78125, 0, 390625, 0, -1953125, 0, 9765625, 0, -48828125, 0, 244140625, 0, -1220703125, 0, 6103515625, 0, -30517578125, 0, 152587890625, 0, ...

MCS13359 : A₀ = 0; A₁ = 1; A_N = - 5 A_N-2 (score: 6)

(Not in OEIS)

Horadam sequence W_n(0, 1; -5, 0), Lucas sequence U_n(0, 5)

25, 51, -299, -713, 4785, 12835, -95699, -282369, 2296777, 7341595, -64309755, -220247849, 2057912161, 7488426867, -74084837795, -284560220945, ...

MCS108549 : A₀ = 0; A₁ = 1; A_K+1 = - 2 K A_K-1 + 1 (score: 5)

25, -125, 625, -3125, 15625, -78125, 390625, -1953125, 9765625, -48828125, 244140625, -1220703125, 6103515625, -30517578125, 152587890625, -762939453125, ...

MCS124400 : A₀ = 1; A_N = - 5 A_N-1 (score: 5)

25, -134, 793, -5564, 44497, -400490, 4004881, -44053712, 528644521, -6872378798, 96213303145, ...

MCS31277 (alias MCS500440) : A₀ = 0; A_K+1 = - K A_K - 2 K + 1 (score: 5)

25, -137, 841, -6031, 49081, -447769, 4526761, -50242151, 607432561, -7946865457, 111863548945, ...

MCS3434886 : A₀ = 1; A₁ = 1; A_K+1 = - K A_K + A_K-1 - K (score: 5)

26, -135, 701, -3640, 18901, -98145, 509626, -2646275, 13741001, -71351280, 370497401, -1923838285, 9989688826, -51872282415, 269351100901, ...

MCS13502 : A₀ = 0; A₁ = 1; A_N = - 5 A_N-1 + A_N-2 (score: 7)

Horadam sequence W_n(0, 1; 1, -5), Lucas sequence U_n(-5, -1)

27, 72, -405, -1296, 8505, 31104, -229635, -933120, 7577955, 33592320, -295540245, -1410877440, 13299311025, 67722117120, -678264862275, ...

MCS1704438 : A₀ = 1; A₁ = 1; A_K+1 = - 3 K A_K-1 (score: 5)

29, -233, 2329, -27949, 391285, -6260561, 112690097, -2253801941, 49583642701, ...

MCS7877 (alias MCS126040, MCS252081) : A₀ = 0; A_K+1 = - 2 K A_K - 1 (score: 4)

29, -260, 2861, -37192, 557881, -9483976, 180195545, -3784106444, 87034448213, ...

MCS31301 : A₀ = 0; A_K+1 = - 2 K A_K + A_K + 1 (score: 5)

29, -260, 2861, -37192, 557881, -9483976, 180195545, -3784106444, 87034448213, ...

MCS501336 : A₀ = 1; A_K+1 = - 2 K A_K - A_K + 1 (score: 5)

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

MCS7789 : A₀ = 0; A_K+1 = - K A_K - A_K - K (score: 4)

32, 0, -384, 0, 6144, 0, -122880, 0, 2949120, 0, -82575360, 0, 2642411520, 0, -95126814720, 0, ...

MCS26629 : A₀ = 0; A₁ = 1; A_K+1 = - 2 K A_K-1 (score: 4)

36, 0, -216, 0, 1296, 0, -7776, 0, 46656, 0, -279936, 0, 1679616, 0, -10077696, 0, 60466176, 0, -362797056, 0, 2176782336, 0, -13060694016, 0, 78364164096, 0, -470184984576, 0, ...

MCS13373 : A₀ = 0; A₁ = 1; A_N = - 6 A_N-2 (score: 7)

Horadam sequence W_n(0, 1; -6, 0), Lucas sequence U_n(0, 6)

39, -271, 1847, -14841, 133487, -1334971, 14684559, -176214853, 2290792919, -32071101063, 481066515719, ...

MCS15757 (alias MCS126060) : A₀ = 0; A_K+1 = - K A_K - K² - 1 (score: 5)

39, -464, 6965, -125364, 2632651, -63183616, 1705957641, -51178729220, ...

MCS15439 (alias MCS247032) : A₀ = 0; A_K+1 = - 3 K A_K + K (score: 5)

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

MCS15437 (alias MCS123500) : A₀ = 0; A_K+1 = - K A_K - K² + K (score: 5)

41, 31, -461, -895, 6481, 22591, -107029, -604031, 1964665, 17669471, -37341149, -567425279, 627491489, 19919950975, -2669742629, -759627879679, -652838174519, ...

MCS3440822 : A₀ = 1; A₁ = 1; A_K+1 = A_K - 2 K A_K-1 (score: 5)

43, -266, 1853, -14834, 133495, -1334962, 14684569, -176214842, 2290792931, -32071101050, 481066515733, ...

MCS15533 : A₀ = 0; A_K+1 = - K A_K + 2 A_K - K (score: 5)

43, -266, 1853, -14834, 133495, -1334962, 14684569, -176214842, 2290792931, -32071101050, 481066515733, ...

MCS31565 (alias MCS505048) : A₀ = 0; A_K+1 = - K A_K + A_K - K - 1 (score: 5)

43, -266, 1853, -14834, 133495, -1334962, 14684569, -176214842, 2290792931, -32071101050, 481066515733, ...

MCS31437 (alias MCS503000) : A₀ = 0; A_K+1 = - K A_K - K - 2 (score: 5)

45, 0, -585, 0, 9945, 0, -208845, 0, 5221125, 0, -151412625, 0, 4996616625, 0, -184874815125, 0, ...

MCS106885 : A₀ = 0; A₁ = 1; A_K+1 = - 2 K A_K-1 - A_K-1 (score: 5)

51, 85, -713, -1359, 12835, 27181, -282369, -652343, 7341595, 18265605, -220247849, -584499359, 7488426867, 21041976925, -284560220945, -841679076999, ...

MCS868397 : A₀ = 0; A₁ = 0; A_K+1 = - 2 K A_K-1 + 1 (score: 5)

52, -473, 5197, -67568, 1013512, -17229713, 327364537, -6874655288, 158117071612, ...

MCS31029 : A₀ = 0; A_K+1 = - 2 K A_K + A_K - K (score: 5)

56, -585, 6984, -97825, 1565136, -28172529, 563450480, -12395910681, 297501856200, ...

MCS15405 (alias MCS123244) : A₀ = 0; A_K+1 = - 2 K A_K - K² (score: 5)

72, 0, -1296, 0, 31104, 0, -933120, 0, 33592320, 0, -1410877440, 0, 67722117120, 0, ...

MCS53263 : A₀ = 0; A₁ = 1; A_K+1 = - 3 K A_K-1 (score: 5)

Complexity level 1 : 1 sequence and 0 aliases.

Complexity level 2 : 12 sequences and 5 aliases.

Complexity level 3 : 90 sequences and 44 aliases.

Complexity level 4 : 545 sequences and 184 aliases.

Complexity level 5 : 2595 sequences and 725 aliases.

Complexity level 6 : 22 sequences and 5 aliases.

Complexity level 7 : 27 sequences and 8 aliases.

Higher complexity levels: 17 sequences.

There are 3309 sequences in the entire catalog.

[1] Neil J. A. Sloane, A Handbook of Integer Sequences, Academic Press (1973), ISBN 0-12-648550-X.

This book encouraged my developing interest in integer sequences, something that was already a hobby at age 9 after beginning to memorize the powers of 2, 3, 5, 6 and 7. It established many of the guidelines I still follow in my catalogs of sequences (notably this project and most of my work documented in nu-sequences), showing how to put sequences in a definitive order and other important ideas.

[2] Neil J.A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press (1995), ISBN 0-12-558630-2.

1 : recurrence relation : I use a broader definition of recurrence relation than some other authors.

For example, the OEIS has an index that includes many linear recurrence relations (go to this page, or start on this page and look for a link starting with "recurrence, linear"). These are sequences that can be described by formulas of the type

A_N = J A_N-1 + K A_N-2 + L A_N-3 + ...

for integer constants J, K, L, ... The precise name for this type of sequence definition is a linear homogeneous recurrence relation with constant coefficients; the sequence generated by it is called a linear recursive sequence.

In addition to those terms, "my" definition of recurrence relation allows constant terms:

... + J + ...

and small integer powers of the sequence index:

... + K N + L N² + ...

and the latter multiplied by a previous term of the sequence:

... + K N A_N-1 + L N A_N-2 + ...

and even the product of two previous terms:

... + K A_N-1 A_N-2 + ...

although not all of these possibilities are represented in this listing.

Quick Index:
      Sequences Beginning 2,0,...
      Sequences Beginning 2,1,...
      Sequences Beginning 2,2,0,... ; 2,2,1,... ; etc.
      Sequences Beginning 2,2,4,... ; 2,2,5,... ; etc.
      Sequences Beginning 2,3,0,... ; 2,3,1,... ; etc.
      Sequences Beginning 2,3,4,... ; 2,3,5,... ; etc.
      Sequences Beginning 2,4,...
      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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