A251759 10-step Fibonacci sequence starting with 0,0,0,0,0,0,0,0,1,0.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1022, 2043, 4084, 8164, 16320, 32624, 65216, 130368, 260608, 520960, 1041409, 2081796, 4161549, 8319014, 16629864, 33243408, 66454192, 132843168, 265555968, 530851328, 1061181696, 2121321983

Offset: 0

Author

Arie Bos, Dec 07 2014

Keywords

• nonn
• easy

Comments

a(n+10) equals the number of n-length binary words avoiding runs of zeros of lengths 10i+9, (i=0,1,2,...). - Milan Janjic, Feb 26 2015

Links

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

Crossrefs

Other 10-step Fibonacci sequences are A251760, A251761, A251762, A251763, A251764, A251765, A251766.

Programs

Mathematica

LinearRecurrence[Table[1, {10}], {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, 45] (* Michael De Vlieger, Dec 08 2014 *)

Formula

a(n+10) = 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) +a(n+9).

G.f.: x^8*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10) . - R. J. Mathar, Mar 28 2025

a(n) = A122265(n+1)-A122265(n). - R. J. Mathar, Mar 28 2025