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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved