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URL: https://oeis.org/A251710

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A251710
7-step Fibonacci sequence starting with (0,0,0,0,0,1,0).
4
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
0,9
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
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
MATHEMATICA
LinearRecurrence[Table[1, {7}], {0, 0, 0, 0, 0, 1, 0}, 40] (* Michael De Vlieger, Dec 09 2014 *)
CROSSREFS
Other 7-step Fibonacci sequences are A066178, A104621, A122189, A251711, A251712, A251713, A251714.
First differences of A122189.
Sequence in context: A239559 A001592 A194629 * A217832 A251740 A251748
KEYWORD
nonn,easy
AUTHOR
Arie Bos, Dec 07 2014
STATUS
approved