OFFSET
0,25
COMMENTS
a(n) = number of compositions of n in which each part is >=12. - Milan Janjic, Jun 28 2010
a(n+23) equals the number of binary words of length n having at least 11 zeros between every two successive ones. - Milan Janjic, Feb 09 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
I. M. Gessel, Ji Li, Compositions and Fibonacci identities, J. Int. Seq. 16 (2013) 13.4.5
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
FORMULA
G.f.: (x-1)/(x-1+x^12). - Alois P. Heinz, Aug 04 2008
For positive integers n and k such that k <= n <= 12*k, and 11 divides n-k, define c(n,k) = binomial(k,(n-k)/11), and c(n,k) = 0, otherwise. Then, for n>=1, a(n+12) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011
MAPLE
a:= n-> (Matrix(12, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [1, 0$10, 1][i], 0)))^n)[12, 12]: seq(a(n), n=0..60); # Alois P. Heinz, Aug 04 2008
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)
CoefficientList[Series[(x - 1) / (x - 1 + x^12), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)
PROG
(PARI) Vec((x-1)/(x-1+x^12)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved