# Minimally Complex Sequences

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)

MCS12864 (alias MCS1646656, MCS1646657, MCS6586637)

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

MCS428289 (alias MCS869505, MCS3499137, MCS3510789)

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

Semifactorials or ''double'' factorials (A6882)

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

Semifactorials or ''double'' factorials (A6882)

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

Semifactorials or ''double'' factorials (A6882)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Quick Index:

mrob27 s.11