A251672 8-step Fibonacci sequence starting with 0,0,0,0,0,0,1,0.

0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 4, 8, 16, 32, 64, 127, 254, 507, 1012, 2020, 4032, 8048, 16064, 32064, 64001, 127748, 254989, 508966, 1015912, 2027792, 4047536, 8079008, 16125952, 32187903, 64248058, 128241127, 255973288, 510930664, 1019833536, 2035619536

Offset: 0

Author

Arie Bos, Dec 06 2014

Keywords

• nonn
• easy

Comments

a(n+8) equals the number of n-length binary words avoiding runs of 0's of lengths 8i+7, (i=0,1,2,...). - Milan Janjic, Feb 26 2015

Links

• G. C. Greubel, 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).

Crossrefs

Other 8-step Fibonacci sequences are A079262, A105754, A251740, A251741, A251742, A251744, A251745.

Programs

Mathematica

LinearRecurrence[Table[1, {8}], {0, 0, 0, 0, 0, 0, 1, 0}, 43] (* Michael De Vlieger, Dec 09 2014 *)

Formula

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

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

a(n) = A079262(n+1)-A079262(n). - R. J. Mathar, Mar 28 2025