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A251710

7-step Fibonacci sequence starting with (0,0,0,0,0,1,0).

0, 0, 0, 0, 0, 1, 0, 1, 2, 4, 8, 16, 32, 63, 126, 251, 500, 996, 1984, 3952, 7872, 15681, 31236, 62221, 123942, 246888, 491792, 979632, 1951392, 3887103, 7742970, 15423719, 30723496, 61200104, 121908416, 242837200, 483723008, 963558913, 1919374856, 3823325993

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OFFSET

0,9

COMMENTS

a(n+7) equals the number of n-length binary words avoiding runs of zeros of lengths 7i+6, (i=0,1,2,...). - Milan Janjic, Feb 26 2015

LINKS

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1).

FORMULA

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

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

a(n) = A066178(n-5) - A066178(n-6). - R. J. Mathar, Mar 28 2025