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Minimally Complex Sequences  


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3, 4, 5, 8, 10, 12, 16, 19, 22, 27, 31, 35, 41, 46, 51, 58, 64, 70, 78, 85, 92, 101, 109, 117, 127, 136, 145, 156, 166, 176, 188, 199, 210, 223, 235, 247, 261, 274, 287, 302, 316, 330, 346, 361, ...

MCS6358070 (alias MCS837665) : A0 = 1; A1 = 1; A2 = 1; AK+1 = AK-2 + K (score: 4)

3, 4, 5, 8, 12, 17, 25, 37, 54, 79, 116, 170, 249, 365, 535, 784, 1149, 1684, 2468, 3617, 5301, 7769, 11386, 16687, 24456, 35842, 52529, 76985, 112827, 165356, 242341, 355168, 520524, 762865, ...

MCS1605892 (alias MCS6423590) : A0 = 1; A1 = 3; A2 = 4; AN = AN-1 + AN-3 (score: 5)

3, 4, 5, 9, 11, 13, 18, 21, 24, 30, 34, 38, 45, 50, 55, 63, 69, 75, 84, 91, 98, 108, 116, 124, 135, 144, 153, 165, 175, 185, 198, 209, 220, 234, 246, 258, 273, 286, 299, 315, 329, 343, 360, 375, ...

MCS6570253 : A0 = 0; A1 = 0; A2 = 0; AK+1 = AK-2 + K + 1 (score: 5)

3, -4, 5, -9, 12, -18, 26, -39, 56, -83, 121, -178, 260, -382, 559, -820, 1201, -1761, 2580, -3782, 5542, -8123, 11904, -17447, 25569, -37474, 54920, -80490, 117963, -172884, 253373, -371337, ...

MCS841777 : A0 = 0; A1 = 1; A2 = 1; AN = - AN-1 - AN-3 - 1 (score: 5)

3, -4, 5, -11, 39, -184, 1065, -7271, 57103, -506656, 5009457, -54597371, 650158995, -8397469564, 116914414901, ...

MCS855428 : A0 = 1; A1 = 3; AK+1 = - K AK - AK-1 (score: 5)

3, 4, 5, -14, -17, -20, 17, 22, 27, -48, -59, -70, 79, 100, 121, -178, -221, -264, 333, 418, 503, -692, -863, -1034, 1355, 1696, 2037, -2742, -3425, -4108, 5449, 6814, 8179, -10936, -13667, ...

MCS25564726 : A0 = 1; A1 = 1; A2 = 1; AK+1 = - 2 AK-2 - K (score: 5)

3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 69, 70, 72, 73, 75, 76, ...

MCS1720 (alias MCS7835) : A0 = 0; A1 = 1; AN = AN-2 + 3 (score: 5)

3, 4, -6, -8, 12, 16, -24, -32, 48, 64, -96, -128, 192, 256, -384, -512, 768, 1024, -1536, -2048, 3072, 4096, -6144, -8192, 12288, 16384, -24576, -32768, 49152, 65536, -98304, -131072, 196608, ...

MCS854787 : A0 = 3; A1 = 4; AN = - 2 AN-2 (score: 5)

Horadam sequence Wn(3, 4; -2, 0)

3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, ...

MCS427267 : A0 = 3; A1 = 4; AN = 2 AN-2 (score: 5)

Horadam sequence Wn(3, 4; 2, 0)

3, 4, 6, 9, 11, 14, 18, 21, 25, 30, 34, 39, 45, 50, 56, 63, 69, 76, 84, 91, 99, 108, 116, 125, 135, 144, 154, 165, 175, 186, 198, 209, 221, 234, 246, 259, 273, 286, 300, 315, 329, 344, 360, 375, ...

MCS1642561 (alias MCS3179033) : A0 = 0; A1 = 0; A2 = 1; AK+1 = AK-2 + K + 1 (score: 5)

3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864, 906, ...

MCS500867 : A0 = 3; AK+1 = AK + K + 1 (score: 5)

3, -4, 6, -9, 13, -19, 28, -41, 60, -88, 129, -189, 277, -406, 595, -872, 1278, -1873, 2745, -4023, 5896, -8641, 12664, -18560, 27201, -39865, 58425, -85626, 125491, -183916, 269542, -395033, ...

MCS405601 (alias MCS1622405, MCS3244825, MCS25958582)

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

3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, -7, 3, 4, ...

MCS865027 : A0 = 3; A1 = 4; AN = - AN-1 - AN-2 (score: 5)

Horadam sequence Wn(3, 4; -1, -1)

3, 4, 7, 9, 13, 16, 21, 25, 31, 36, 43, 49, 57, 64, 73, 81, 91, 100, 111, 121, 133, 144, 157, 169, 183, 196, 211, 225, 241, 256, 273, 289, 307, 324, 343, 361, 381, 400, 421, 441, 463, 484, 507, ...

MCS836 (alias MCS3478022, MCS13996550, MCS14043158)

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

N2/4, rounded up (A4652)

3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, ...

MCS860676 (alias MCS860675) : A0 = 1; A1 = 3; AN = AN-1 + AN-2 (score: 4)

Lucas numbers (A0204)

Horadam sequence Wn(1, 3; 1, 1) ; Horadam sequence Wn(3, 4; 1, 1)

3, 4, 7, 12, 19, 28, 39, 52, 67, 84, 103, 124, 147, 172, 199, 228, 259, 292, 327, 364, 403, 444, 487, 532, 579, 628, 679, 732, 787, 844, 903, 964, 1027, 1092, 1159, 1228, 1299, 1372, 1447, 1524, ...

MCS3548 : AK = K2 + 3 (score: 5)

3, 4, 8, 10, 15, 18, 24, 28, 35, 40, 48, 54, 63, 70, 80, 88, 99, 108, 120, 130, 143, 154, 168, 180, 195, 208, 224, 238, 255, 270, 288, 304, 323, 340, 360, 378, 399, 418, 440, 460, 483, 504, 528, ...

MCS1746049 (alias MCS6852653) : A0 = 0; A1 = 0; AK+1 = AK-1 + K + 2 (score: 5)

3, 4, 9, 12, 19, 24, 33, 40, 51, 60, 73, 84, 99, 112, 129, 144, 163, 180, 201, 220, 243, 264, 289, 312, 339, 364, 393, 420, 451, 480, 513, 544, 579, 612, 649, 684, 723, 760, 801, 840, 883, 924, ...

MCS31340 (alias MCS501384, MCS6858774) : A0 = 0; AK+1 = - AK + K2 - K + 1 (score: 5)

3, 4, 9, 12, 23, 30, 53, 68, 115, 146, 241, 304, 495, 622, 1005, 1260, 2027, 2538, 4073, 5096, 8167, 10214, 16357, 20452, 32739, 40930, 65505, 81888, 131039, 163806, 262109, 327644, 524251, ...

MCS1713414 : A0 = 1; A1 = 1; AK+1 = 2 AK-1 + K (score: 4)

3, 4, -10, -18, 77, 152, -684, -1510, 7535, 18132, -97942, -253834, 1469145, 4061360, -24975448, -73104462, 474533531, 1462089260, -9965204130, -32165963698, 229199695013, 771983128776, ...

MCS856118 : A0 = 1; A1 = 1; AK+1 = - K AK-1 + K (score: 4)

3, 4, 10, 22, 62, 172, 544, 1748, 6100, 21832, 82832, 322984, 1316968, 5515760, 23953312, 106689712, 489942704, 2303667808, 11122636480, 54892324832, 277345054432, ...

MCS860196 : A0 = 1; A1 = 3; AK+1 = AK + K AK-1 (score: 5)

3, 4, -11, -14, 15, 20, -39, -50, 67, 88, -147, -190, 279, 364, -575, -746, 1131, 1472, -2283, -2966, 4543, 5908, -9111, -11842, 18195, 23656, -36419, -47342, 72807, 94652, -145647, -189338, ...

MCS3435270 : A0 = 1; A1 = 1; AK+1 = - 2 AK-1 - K (score: 4)

3, -4, 11, -18, 41, -76, 159, -310, 629, -1248, 2507, -5002, 10017, -20020, 40055, -80094, 160205, -320392, 640803, -1281586, 2563193, -5126364, 10252751, -20505478, 41010981, -82021936, ...

MCS1002305 : A0 = -1; AK+1 = - 2 AK + K + 1 (score: 5)

3, 4, 11, 18, 57, 110, 401, 882, 3611, 8822, 39723, 105866, 516401, 1482126, 7746017, 23714018, 131682291, 426852326, 2501963531, 8537046522, 52541234153, 187815023486, ...

MCS1744934 : A0 = 1; A1 = 1; AK+1 = K AK-1 + 2 (score: 5)

3, 4, 11, 37, 159, 832, 5151, 36889, 300263, 2739256, 27692823, 307360309, 3716016531, 48615575212, 684334069499, ...

MCS854276 : A0 = 1; A1 = 3; AK+1 = K AK + AK-1 (score: 5)

3, 4, 13, 18, 31, 40, 57, 70, 91, 108, 133, 154, 183, 208, 241, 270, 307, 340, 381, 418, 463, 504, 553, 598, 651, 700, 757, 810, 871, 928, 993, 1054, 1123, 1188, 1261, 1330, 1407, 1480, 1561, ...

MCS252692 : A0 = 1; AK+1 = - AK + 2 K2 - 1 (score: 5)

3, 4, 13, 21, 79, 148, 633, 1333, 6331, 14664, 75973, 190633, 1063623, 2859496, 17017969, 48611433, 306323443, 923617228, 6126468861, 19395961789, 134782314943, 446107121148, ...

MCS869129 : A0 = 0; A1 = 0; AK+1 = K AK-1 - AK-1 + 1 (score: 5)

3, 4, 13, 21, 79, 148, 633, 1333, 6331, 14664, 75973, 190633, 1063623, 2859496, 17017969, 48611433, 306323443, 923617228, 6126468861, 19395961789, 134782314943, 446107121148, ...

MCS13568 : A0 = 0; A1 = 1; AK+1 = K AK-1 + 1 (score: 4)

3, 4, 13, 21, 79, 148, 633, 1333, 6331, 14664, 75973, 190633, 1063623, 2859496, 17017969, 48611433, 306323443, 923617228, 6126468861, 19395961789, 134782314943, 446107121148, ...

MCS3475494 : A0 = 1; A1 = 1; AK+1 = K AK-1 + AK-1 + 1 (score: 5)

3, 4, 13, 23, 82, 174, 679, 1648, 6964, 18807, 85216, 251455, 1211831, 3857041, 19640751, 66781528, 357390559, 1288489783, 7214592708, 27415676002, 160009529359, 637775140754, ...

MCS6296118 : A0 = 1; A1 = 1; A2 = 1; AK+1 = K AK-1 + AK-2 (score: 5)

3, 4, 15, 24, 105, 192, 945, 1920, 10395, 23040, 135135, 322560, 2027025, 5160960, 34459425, 92897280, 654729075, 1857945600, 13749310575, 40874803200, 316234143225, 980995276800, ...

MCS1709094 : A0 = 1; A1 = 1; AK+1 = K AK-1 + 2 AK-1 (score: 5)

3, 4, -19, -29, 151, 260, -1511, -2861, 18131, 37192, -253835, -557881, 4061359, 9483976, -73104463, -180195545, 1462089259, 3784106444, -32165963699, -87034448213, 771983128775, ...

MCS877325 : A0 = 0; A1 = 0; AK+1 = - K AK-1 - AK-1 - 1 (score: 5)

3, 4, -19, -29, 151, 260, -1511, -2861, 18131, 37192, -253835, -557881, 4061359, 9483976, -73104463, -180195545, 1462089259, 3784106444, -32165963699, -87034448213, 771983128775, ...

MCS438297 : A0 = -1; A1 = 0; AK+1 = - K AK-1 - 1 (score: 5)

3, 4, -20, -30, 133, 232, -1206, -2330, 13255, 27948, -172328, -391286, 2584905, 6260560, -43943402, -112690098, 834924619, 2253801940, -17533417020, -49583642702, 403268591437, ...

MCS3432662 : A0 = 1; A1 = 0; AK+1 = - K AK-1 - K (score: 5)

3, 4, 20, 30, 147, 248, 1332, 2490, 14663, 29892, 190632, 418502, 2859495, 6696048, 48611432, 120528882, 923617227, 2410577660, 19395961788, 53032708542, 446107121147, ...

MCS1712205 : A0 = -1; A1 = -1; AK+1 = K AK-1 + K (score: 5)

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

MCS3463940 : A0 = 1; A1 = 3; AK+1 = - AK - AK-1 - K (score: 5)

3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, 5, 1, 3, ...

MCS1573924 : A0 = 1; A1 = 3; A2 = 5; AN = AN-3 (score: 5)

3, 5, -1, -3, -5, 1, 3, 5, -1, -3, -5, 1, 3, 5, -1, -3, -5, 1, 3, 5, -1, -3, -5, 1, 3, 5, -1, -3, -5, 1, 3, 5, -1, -3, -5, 1, 3, 5, -1, -3, -5, 1, 3, 5, -1, -3, -5, 1, 3, 5, -1, -3, -5, 1, 3, 5, ...

MCS1574436 : A0 = 1; A1 = 3; A2 = 5; AN = - AN-3 (score: 5)

3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, 1, 3, -5, ...

MCS3519236 : A0 = 1; A1 = 3; AN = - AN-1 - AN-2 - 1 (score: 5)

3, -5, -1, 11, -9, -13, 31, -5, -57, 67, 47, -181, 87, 275, -449, -101, 999, -797, -1201, 2795, -393, -5197, 5983, 4411, -16377, 7555, 25199, -40309, -10089, 90707, -70529, -110885, 251943, ...

MCS3459844 : A0 = 1; A1 = 3; AN = - AN-1 - 2 AN-2 (score: 5)

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

3, 5, 3, 3, 7, 9, 7, 7, 11, 13, 11, 11, 15, 17, 15, 15, 19, 21, 19, 19, 23, 25, 23, 23, 27, 29, 27, 27, 31, 33, 31, 31, 35, 37, 35, 35, 39, 41, 39, 39, 43, 45, 43, 43, 47, 49, 47, 47, 51, 53, 51, ...

MCS3429901 : A0 = -1; A1 = -1; AK+1 = - AK-1 + 2 K (score: 5)

3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, ...

MCS854035 : A0 = 3; A1 = 5; AN = AN-2 (score: 5)

Horadam sequence Wn(3, 5; 1, 0)

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

MCS855059 : A0 = 3; A1 = 5; AN = - AN-2 (score: 5)

Horadam sequence Wn(3, 5; -1, 0)

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

MCS503171 : A0 = 3; AN = - AN-1 - 2 (score: 5)

3, 5, 4, 4, 7, 9, 8, 8, 11, 13, 12, 12, 15, 17, 16, 16, 19, 21, 20, 20, 23, 25, 24, 24, 27, 29, 28, 28, 31, 33, 32, 32, 35, 37, 36, 36, 39, 41, 40, 40, 43, 45, 44, 44, 47, 49, 48, 48, 51, 53, 52, ...

MCS1739457 : A0 = 0; A1 = 0; AK+1 = - AK-1 + 2 K + 1 (score: 5)

3, -5, -4, 7, -2, -12, 8, 9, -21, -2, 29, -20, -32, 48, 11, -81, 36, 91, -118, -56, 208, -63, -265, 270, 201, -536, 68, 736, -605, -669, 1340, 63, -2010, 1276, 2072, -3287, -797, 5358, -2491, ...

MCS1674305 : A0 = 0; A1 = 0; A2 = 1; AN = - AN-2 + AN-3 - 1 (score: 5)

3, 5, 5, 5, 7, 9, 9, 9, 11, 13, 13, 13, 15, 17, 17, 17, 19, 21, 21, 21, 23, 25, 25, 25, 27, 29, 29, 29, 31, 33, 33, 33, 35, 37, 37, 37, 39, 41, 41, 41, 43, 45, 45, 45, 47, 49, 49, 49, 51, 53, 53, ...

MCS1714950 : A0 = 1; A1 = 1; AK+1 = - AK-1 + 2 K (score: 4)

3, -5, 5, -9, 9, -15, 17, -25, 31, -43, 55, -75, 97, -131, 171, -229, 301, -401, 529, -703, 929, -1233, 1631, -2163, 2863, -3795, 5025, -6659, 8819, -11685, 15477, -20505, 27161, -35983, 47665, ...

MCS26773046 : A0 = 1; A1 = 1; A2 = 1; AN = AN-2 - AN-3 - 1 (score: 5)

3, 5, 6, 6, 5, 3, 0, -4, -9, -15, -22, -30, -39, -49, -60, -72, -85, -99, -114, -130, -147, -165, -184, -204, -225, -247, -270, -294, -319, -345, -372, -400, -429, -459, -490, -522, -555, -589, ...

MCS7913 : A0 = 0; AK+1 = AK - K + 3 (score: 5)

3, 5, 6, 6, 6, 7, 9, 11, 12, 12, 12, 13, 15, 17, 18, 18, 18, 19, 21, 23, 24, 24, 24, 25, 27, 29, 30, 30, 30, 31, 33, 35, 36, 36, 36, 37, 39, 41, 42, 42, 42, 43, 45, 47, 48, 48, 48, 49, 51, 53, 54, ...

MCS861377 (alias MCS27209, MCS3515585) : A0 = 0; A1 = 0; AK+1 = AK - AK-1 + K (score: 4)

3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 24, 25, 27, 29, 30, 31, 33, 35, 36, 37, 39, 41, 42, 43, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 63, 65, 66, 67, 69, 71, 72, 73, 75, 77, ...

MCS3357 : A0 = 0; A1 = 1; AK+1 = - AK-1 + 3 K (score: 5)

3, 5, 6, 9, 12, 14, 18, 22, 25, 30, 35, 39, 45, 51, 56, 63, 70, 76, 84, 92, 99, 108, 117, 125, 135, 145, 154, 165, 176, 186, 198, 210, 221, 234, 247, 259, 273, 287, 300, 315, 330, 344, 360, 376, ...

MCS794753 (alias MCS821281) : A0 = -1; A1 = 0; A2 = 1; AK+1 = AK-2 + K (score: 5)

3, 5, 7, 7, 7, 7, 9, 11, 13, 13, 13, 13, 15, 17, 19, 19, 19, 19, 21, 23, 25, 25, 25, 25, 27, 29, 31, 31, 31, 31, 33, 35, 37, 37, 37, 37, 39, 41, 43, 43, 43, 43, 45, 47, 49, 49, 49, 49, 51, 53, 55, ...

MCS12748342 : A0 = 1; A1 = 1; A2 = 1; AK+1 = - AK-2 + 2 K (score: 5)

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, ...

MCS3538 (alias MCS3546, MCS7098, MCS28410, MCS62784, MCS125569, MCS251139, MCS1002160, MCS1725188)

AK = 2 K + 1 (score: 3)

Odd numbers (A5408)

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

3, -5, 7, -9, 11, -13, 15, -17, 19, -21, 23, -25, 27, -29, 31, -33, 35, -37, 39, -41, 43, -45, 47, -49, 51, -53, 55, -57, 59, -61, 63, -65, 67, -69, 71, -73, 75, -77, 79, -81, 83, -85, 87, -89, ...

MCS6907405 : A0 = -1; A1 = -1; AN = - 2 AN-1 - AN-2 (score: 5)

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

3, 5, 7, 11, 17, 25, 37, 55, 81, 119, 175, 257, 377, 553, 811, 1189, 1743, 2555, 3745, 5489, 8045, 11791, 17281, 25327, 37119, 54401, 79729, 116849, 171251, 250981, 367831, 539083, 790065, ...

MCS26346550 : A0 = 1; A1 = 1; A2 = 1; AN = AN-1 + AN-3 + 1 (score: 5)

3, 5, 7, 13, 23, 37, 63, 109, 183, 309, 527, 893, 1511, 2565, 4351, 7373, 12503, 21205, 35951, 60957, 103367, 175269, 297183, 503917, 854455, 1448821, 2456655, 4165565, 7063207, 11976517, ...

MCS401489 (alias MCS802977, MCS12847670) : A0 = 0; A1 = 1; A2 = 1; AN = AN-1 + 2 AN-3 (score: 5)

3, 5, 8, 10, 11, 10, 8, 6, 6, 9, 15, 22, 27, 27, 21, 11, 2, 0, 9, 28, 50, 64, 60, 35, -3, -36, -43, -11, 55, 129, 172, 150, 55, -82, -196, -214, -94, 141, 395, 530, 431, 79, -407, -793, -826, ...

MCS804913 : A0 = 0; A1 = 1; A2 = 1; AK+1 = AK - AK-2 + K (score: 5)

3, 5, 8, 11, 15, 19, 24, 29, 35, 41, 48, 55, 63, 71, 80, 89, 99, 109, 120, 131, 143, 155, 168, 181, 195, 209, 224, 239, 255, 271, 288, 305, 323, 341, 360, 379, 399, 419, 440, 461, 483, 505, 528, ...

MCS1713165 (alias MCS6820, MCS1739009, MCS7021581)

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

3, 5, 8, 12, 16, 21, 27, 33, 40, 48, 56, 65, 75, 85, 96, 108, 120, 133, 147, 161, 176, 192, 208, 225, 243, 261, 280, 300, 320, 341, 363, 385, 408, 432, 456, 481, 507, 533, 560, 588, 616, 645, 675, ...

MCS865057 : A0 = 0; A1 = 0; AK+1 = - AK - AK-1 + K2 (score: 5)

3, 5, 8, 13, 19, 28, 40, 56, 78, 107, 146, 198, 267, 359, 481, 643, 858, 1143, 1521, 2022, 2686, 3566, 4732, 6277, 8324, 11036, 14629, 19389, 25695, 34049, 45116, 59777, 79199, 104928, 139012, ...

MCS795681 : A0 = 0; A1 = 1; A2 = 1; AK+1 = AK-1 + AK-2 + K (score: 5)

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, ...

MCS432385 (alias MCS864773, MCS1729545, MCS1729549)

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

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

3, 5, 9, 13, 19, 25, 33, 41, 51, 61, 73, 85, 99, 113, 129, 145, 163, 181, 201, 221, 243, 265, 289, 313, 339, 365, 393, 421, 451, 481, 513, 545, 579, 613, 649, 685, 723, 761, 801, 841, 883, 925, ...

MCS1714694 : A0 = 1; A1 = 1; AK+1 = AK-1 + 2 K (score: 4)

3, -5, 9, -15, 25, -41, 67, -109, 177, -287, 465, -753, 1219, -1973, 3193, -5167, 8361, -13529, 21891, -35421, 57313, -92735, 150049, -242785, 392835, -635621, 1028457, -1664079, 2692537, ...

MCS25887798 : A0 = 1; A1 = 1; A2 = 1; AN = - 2 AN-1 + AN-3 (score: 5)

3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049, 242785, 392835, 635621, 1028457, 1664079, 2692537, 4356617, 7049155, ...

MCS3482118 (alias MCS3482116) : A0 = 1; A1 = 1; AN = AN-1 + AN-2 + 1 (score: 4)

3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201, 2209, 4063, 7473, 13745, 25281, 46499, 85525, 157305, 289329, 532159, 978793, 1800281, 3311233, 6090307, 11201821, 20603361, 37895489, 69700671, ...

MCS25723958 : A0 = 1; A1 = 1; A2 = 1; AN = AN-1 + AN-2 + AN-3 (score: 5)

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, ...

MCS252547 : A0 = 3; AN = 2 AN-1 - 1 (score: 5)

3, 5, 10, 14, 21, 27, 36, 44, 55, 65, 78, 90, 105, 119, 136, 152, 171, 189, 210, 230, 253, 275, 300, 324, 351, 377, 406, 434, 465, 495, 528, 560, 595, 629, 666, 702, 741, 779, 820, 860, 903, 945, ...

MCS15572 (alias MCS252689, MCS498376, MCS1739393)

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

3, 5, 10, 18, 32, 55, 93, 155, 256, 420, 686, 1117, 1815, 2945, 4774, 7734, 12524, 20275, 32817, 53111, 85948, 139080, 225050, 364153, 589227, 953405, 1542658, 2496090, 4038776, 6534895, 10573701, ...

MCS3445252 : A0 = 1; A1 = 3; AK+1 = AK + AK-1 + K (score: 5)

3, -5, 11, -21, 43, -85, 171, -341, 683, -1365, 2731, -5461, 10923, -21845, 43691, -87381, 174763, -349525, 699051, -1398101, 2796203, -5592405, 11184811, -22369621, 44739243, -89478485, ...

MCS1957 (alias MCS3378, MCS125280, MCS250561, MCS501123)

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

A77925

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

3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971, 357913941, ...

MCS3362 (alias MCS1721604, MCS1721606) : A0 = 0; A1 = 1; AN = AN-1 + 2 AN-2 (score: 4)

Jacobsthal sequence (A1045)

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

3, 5, 13, 19, 31, 41, 57, 71, 91, 109, 133, 155, 183, 209, 241, 271, 307, 341, 381, 419, 463, 505, 553, 599, 651, 701, 757, 811, 871, 929, 993, 1055, 1123, 1189, 1261, 1331, 1407, 1481, 1561, ...

MCS62228 : A0 = 1; AK+1 = - AK + 2 K2 (score: 4)

3, 5, 13, 25, 71, 157, 505, 1265, 4555, 12661, 50117, 151945, 651535, 2127245, 9773041, 34035937, 166141715, 612646885, 3156692605, 12252937721, 66290544727, 269564629885, ...

MCS53552 (alias MCS3427366) : A0 = 0; A1 = 1; AK+1 = K AK-1 - AK-1 + K (score: 5)

3, 5, 13, 25, 71, 157, 505, 1265, 4555, 12661, 50117, 151945, 651535, 2127245, 9773041, 34035937, 166141715, 612646885, 3156692605, 12252937721, 66290544727, 269564629885, ...

MCS3477542 : A0 = 1; A1 = 1; AK+1 = K AK-1 + K + 1 (score: 5)

3, -5, 13, -31, 75, -181, 437, -1055, 2547, -6149, 14845, -35839, 86523, -208885, 504293, -1217471, 2939235, -7095941, 17131117, -41358175, 99847467, -241053109, 581953685, -1404960479, ...

MCS3453444 : A0 = 1; A1 = 3; AN = - 2 AN-1 + AN-2 (score: 5)

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

3, 5, 15, 29, 95, 209, 767, 1889, 7679, 20789, 92159, 270269, 1290239, 4054049, 20643839, 68918849, 371589119, 1309458149, 7431782399, 27498621149, 163499212799, 632468286449, ...

MCS3426342 : A0 = 1; A1 = 1; AK+1 = K AK-1 + AK-1 + K (score: 5)

3, 5, 15, 29, 95, 209, 767, 1889, 7679, 20789, 92159, 270269, 1290239, 4054049, 20643839, 68918849, 371589119, 1309458149, 7431782399, 27498621149, 163499212799, 632468286449, ...

MCS3510310 : A0 = 1; A1 = 1; AK+1 = K AK-1 + K - 1 (score: 5)

3, 5, 19, 41, 191, 493, 2675, 7889, 48151, 157781, 1059323, 3786745, 27542399, 106028861, 826271971, 3392923553, 28093247015, 122145247909, ...

MCS1736790 : A0 = 1; A1 = 1; AK+1 = 2 K AK-1 + 1 (score: 5)

3, 5, 21, 45, 231, 585, 3465, 9945, 65835, 208845, 1514205, 5221125, 40883535, 151412625, 1267389585, 4996616625, 44358635475, 184874815125, ...

MCS1708118 : A0 = 1; A1 = 1; AK+1 = 2 K AK-1 + AK-1 (score: 5)

3, 5, 21, 45, 231, 585, 3465, 9945, 65835, 208845, 1514205, 5221125, 40883535, 151412625, 1267389585, 4996616625, 44358635475, 184874815125, ...

MCS1710166 : A0 = 1; A1 = 1; AK+1 = 2 K AK-1 - AK-1 (score: 5)

3, -5, 21, -95, 555, -3783, 29717, -263661, 2606903, -28412261, 338340241, -4370010859, 60841811799, -908257166111, ...

MCS3427718 : A0 = 1; A1 = 1; AK+1 = - K AK - AK-1 + K (score: 5)

3, 5, 23, 49, 275, 685, 4399, 12329, 87979, 271237, 2111495, 7052161, 59121859, 211564829, 1891899487, 7193204185, 68108381531, 273341759029, ...

MCS1753174 : A0 = 1; A1 = 1; AK+1 = 2 K AK-1 - 1 (score: 5)

3, -5, 29, -129, 799, -5557, 44505, -400481, 4004891, -44053701, 528644533, -6872378785, 96213303159, ...

MCS124520 : A0 = 1; AK+1 = - K AK - AK + K2 (score: 5)

3, -6, 5, -9, 7, -12, 9, -15, 11, -18, 13, -21, 15, -24, 17, -27, 19, -30, 21, -33, 23, -36, 25, -39, 27, -42, 29, -45, 31, -48, 33, -51, 35, -54, 37, -57, 39, -60, 41, -63, 43, -66, 45, -69, 47, ...

MCS26989 : A0 = 0; A1 = 1; AK+1 = - 2 AK - AK-1 - K (score: 5)

3, 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, ...

MCS62360 : A0 = 1; AK+1 = - K AK + 3 AK (score: 5)

3, 6, 6, 2, -5, -12, -15, -11, 0, 14, 24, 23, 8, -17, -41, -50, -34, 6, 55, 88, 81, 25, -64, -146, -172, -109, 36, 207, 315, 278, 70, -246, -525, -596, -351, 173, 768, 1118, 944, 175, -944, -1889, ...

MCS839729 : A0 = 0; A1 = 1; A2 = 1; AN = AN-1 - AN-3 - 1 (score: 5)

3, 6, 6, 6, 9, 12, 12, 12, 15, 18, 18, 18, 21, 24, 24, 24, 27, 30, 30, 30, 33, 36, 36, 36, 39, 42, 42, 42, 45, 48, 48, 48, 51, 54, 54, 54, 57, 60, 60, 60, 63, 66, 66, 66, 69, 72, 72, 72, 75, 78, ...

MCS429761 : A0 = 0; A1 = 0; AK+1 = - AK-1 + 3 K (score: 5)

3, 6, 7, 6, 5, 6, 9, 12, 13, 12, 11, 12, 15, 18, 19, 18, 17, 18, 21, 24, 25, 24, 23, 24, 27, 30, 31, 30, 29, 30, 33, 36, 37, 36, 35, 36, 39, 42, 43, 42, 41, 42, 45, 48, 49, 48, 47, 48, 51, 54, 55, ...

MCS3445509 : A0 = 0; A1 = -1; AK+1 = AK - AK-1 + K (score: 5)

3, 6, 7, 12, 17, 20, 27, 34, 39, 48, 57, 64, 75, 86, 95, 108, 121, 132, 147, 162, 175, 192, 209, 224, 243, 262, 279, 300, 321, 340, 363, 386, 407, 432, 457, 480, 507, 534, 559, 588, 617, 644, 675, ...

MCS13516 : A0 = 0; A1 = 1; AK+1 = - AK - AK-1 + K2 (score: 5)

3, 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, ...

MCS27087 : 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)

3, 6, 9, 10, 5, -14, -63, -174, -411, -902, -1903, -3926, -7995, -16158, -32511, -65246, -130747, -261782, -523887, -1048134, -2096667, -4193774, -8388031, -16776590, -33553755, -67108134, ...

MCS250508 : A0 = 1; AK+1 = 2 AK - K2 + 1 (score: 5)

3, 6, 9, 11, 11, 9, 6, 4, 5, 10, 18, 26, 30, 27, 17, 4, -5, -3, 13, 39, 64, 74, 59, 20, -28, -60, -52, 5, 95, 178, 205, 143, -1, -171, -278, -240, -31, 286, 566, 638, 394, -129, -723, -1072, -897, ...

MCS1609825 : A0 = 0; A1 = 0; A2 = 1; AK+1 = AK - AK-2 + K (score: 5)

3, 6, 9, 11, 12, 13, 15, 18, 21, 23, 24, 25, 27, 30, 33, 35, 36, 37, 39, 42, 45, 47, 48, 49, 51, 54, 57, 59, 60, 61, 63, 66, 69, 71, 72, 73, 75, 78, 81, 83, 84, 85, 87, 90, 93, 95, 96, 97, 99, ...

MCS13461 : A0 = 0; A1 = 1; AK+1 = AK - AK-1 + 2 K (score: 5)

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, ...

MCS883 (alias MCS494) : AK = 3 K (score: 3)

Multiples of 3 (A8585)

3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, ...

MCS484 (alias MCS1944, MCS1956, MCS6794, MCS13609, MCS126240, MCS251168, MCS1742017, MCS1755777)

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

Triangular numbers (A0217)

3, 6, 11, 19, 31, 49, 76, 116, 175, 262, 390, 578, 854, 1259, 1853, 2724, 4001, 5873, 8617, 12639, 18534, 27174, 39837, 58396, 85596, 125460, 183884, 269509, 394999, 578914, 848455, 1243487, ...

MCS1609793 : A0 = 0; A1 = 0; A2 = 1; AK+1 = AK + AK-2 + K (score: 5)

3, 6, 11, 19, 32, 53, 87, 142, 231, 375, 608, 985, 1595, 2582, 4179, 6763, 10944, 17709, 28655, 46366, 75023, 121391, 196416, 317809, 514227, 832038, 1346267, 2178307, 3524576, 5702885, 9227463, ...

MCS6824 : A0 = 0; A1 = 1; AN = AN-1 + AN-2 + 2 (score: 5)

3, 6, 11, 20, 37, 70, 135, 264, 521, 1034, 2059, 4108, 8205, 16398, 32783, 65552, 131089, 262162, 524307, 1048596, 2097173, 4194326, 8388631, 16777240, 33554457, 67108890, 134217755, 268435484, ...

MCS250544 (alias MCS248515) : A0 = 1; AK+1 = 2 AK - K + 1 (score: 4)

3, -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, ...

MCS497347 (alias MCS1002337) : A0 = 3; AK+1 = - 2 AK - K (score: 5)

3, 6, 12, 18, 27, 36, 48, 60, 75, 90, 108, 126, 147, 168, 192, 216, 243, 270, 300, 330, 363, 396, 432, 468, 507, 546, 588, 630, 675, 720, 768, 816, 867, 918, 972, 1026, 1083, 1140, 1200, 1260, ...

MCS429697 : A0 = 0; A1 = 0; AK+1 = AK-1 + 3 K (score: 5)

3, 6, 12, 22, 39, 67, 113, 188, 310, 508, 829, 1349, 2191, 3554, 5760, 9330, 15107, 24455, 39581, 64056, 103658, 167736, 271417, 439177, 710619, 1149822, 1860468, 3010318, 4870815, 7881163, ...

MCS3445254 (alias MCS13732) : A0 = 1; A1 = 1; AK+1 = AK + AK-1 + K (score: 4)

3, 6, 12, 23, 41, 68, 106, 157, 223, 306, 408, 531, 677, 848, 1046, 1273, 1531, 1822, 2148, 2511, 2913, 3356, 3842, 4373, 4951, 5578, 6256, 6987, 7773, 8616, 9518, 10481, 11507, 12598, 13756, ...

MCS251144 : A0 = 1; AK+1 = AK + K2 + 2 (score: 5)

3, -6, 12, -24, 48, -96, 192, -384, 768, -1536, 3072, -6144, 12288, -24576, 49152, -98304, 196608, -393216, 786432, -1572864, 3145728, -6291456, 12582912, -25165824, 50331648, -100663296, ...

MCS124291 : A0 = 3; AN = - 2 AN-1 (score: 4)

3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, ...

MCS62083 : A0 = 3; AN = 2 AN-1 (score: 4)

3 Times a Power of 2 (A7283)

3, 6, 13, 20, 31, 42, 57, 72, 91, 110, 133, 156, 183, 210, 241, 272, 307, 342, 381, 420, 463, 506, 553, 600, 651, 702, 757, 812, 871, 930, 993, 1056, 1123, 1190, 1261, 1332, 1407, 1482, 1561, ...

MCS250644 : A0 = 1; AK+1 = - AK + 2 K2 + 1 (score: 5)

3, 6, 13, 23, 39, 60, 89, 125, 171, 226, 293, 371, 463, 568, 689, 825, 979, 1150, 1341, 1551, 1783, 2036, 2313, 2613, 2939, 3290, 3669, 4075, 4511, 4976, 5473, 6001, 6563, 7158, 7789, 8455, 9159, ...

MCS3475590 : A0 = 1; A1 = 1; AK+1 = AK-1 + K2 + 1 (score: 5)

3, -6, 13, -24, 51, -98, 201, -396, 799, -1590, 3189, -6368, 12747, -25482, 50977, -101940, 203895, -407774, 815565, -1631112, 3262243, -6524466, 13048953, -26097884, 52195791, -104391558, ...

MCS31446 (alias MCS497283) : A0 = 0; AK+1 = - 2 AK + K - 2 (score: 5)


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Quick Index:
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