A251746 9-step Fibonacci sequence starting with 0,0,0,0,0,0,0,1,0.

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 4, 8, 16, 32, 64, 128, 255, 510, 1019, 2036, 4068, 8128, 16240, 32448, 64832, 129536, 258817, 517124, 1033229, 2064422, 4124776, 8241424, 16466608, 32900768, 65736704, 131343872, 262428927, 524340730, 1047648231, 2093232040

Offset: 0

Author

Arie Bos, Dec 07 2014

Keywords

• nonn
• easy

Comments

a(n+9) equals the number of n-length binary words avoiding runs of zeros of lengths 9i+8, (i=0,1,2,...). - Milan Janjic, Feb 26 2015

Links

• Robert Price, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1).

Crossrefs

Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251747, A251748, A251749, A251750, A251751, A251752.

Cf. A255530 (Indices of primes in this sequence).

Programs

Mathematica

LinearRecurrence[Table[1, {9}], {0, 0, 0, 0, 0, 0, 0, 1, 0}, 44] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).

G.f.: x^7*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025

a(n) = A104144(n+1)-A104144(n). - R. J. Mathar, Mar 28 2025