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 A017908 Expansion of 1/(1 - x^14 - x^15 - ...). 2
 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 20, 24, 29, 35, 42, 50, 59, 69, 80, 92, 105, 119, 134, 151, 171, 195, 224, 259, 301, 351, 410, 479, 559, 651, 756, 875, 1009 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,29 COMMENTS a(n) = number of compositions of n in which each part is >=14. - Milan Janjic, Jun 28 2010 a(n+27) equals the number of binary words of length n having at least 13 zeros between every two successive ones. - Milan Janjic, Feb 09 2015 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1). FORMULA G.f.: (x-1)/(x-1+x^14). - Alois P. Heinz, Aug 04 2008 For positive integers n and k such that k <= n <= 14*k, and 13 divides n-k, define c(n,k) = binomial(k,(n-k)/13), and c(n,k) = 0, otherwise. Then, for n>=1,  a(n+14) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011 MAPLE a:= n-> (Matrix(14, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0\$12, 1][i] else 0 fi)^n)[14, 14]: seq(a(n), n=0..62); # Alois P. Heinz, Aug 04 2008 MATHEMATICA LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *) PROG (PARI) Vec((x-1)/(x-1+x^14)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012 CROSSREFS Sequence in context: A033067 A032512 A050723 * A044965 A044827 A048313 Adjacent sequences:  A017905 A017906 A017907 * A017909 A017910 A017911 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 20 12:57 EST 2019. Contains 320327 sequences. (Running on oeis4.)