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

Offset: 0

Author

Arie Bos, Dec 07 2014

Keywords

• nonn
• easy

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

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

Crossrefs

Other 7-step Fibonacci sequences are A066178, A104621, A122189, A251711, A251712, A251713, A251714.

Programs

J

NB. see A251713 for the program and apply it to 0 0 0 0 0 1 0.

Mathematica

LinearRecurrence[Table[1, {7}], {0, 0, 0, 0, 0, 1, 0}, 40] (* Michael De Vlieger, Dec 09 2014 *)

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