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URL: https://oeis.org/A251759

⇱ A251759 - OEIS

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A251759
10-step Fibonacci sequence starting with 0,0,0,0,0,0,0,0,1,0.
7
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
0,12
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
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
MATHEMATICA
LinearRecurrence[Table[1, {10}], {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, 45] (* Michael De Vlieger, Dec 08 2014 *)
CROSSREFS
Other 10-step Fibonacci sequences are A251760, A251761, A251762, A251763, A251764, A251765, A251766.
Sequence in context: A258800 A194632 A282584 * A243087 A123464 A113019
KEYWORD
nonn,easy
AUTHOR
Arie Bos, Dec 07 2014
STATUS
approved