A017906 Expansion of 1/(1 - x^12 - x^13 - ...).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 22, 27, 33, 40, 48, 57, 67, 78, 90, 103, 118, 136, 158, 185, 218, 258, 306, 363, 430, 508, 598, 701, 819, 955, 1113, 1298, 1516, 1774

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

Sequence in context: A269445 A330513 A246092 * A159452 A044963 A044825

Adjacent sequences: A017903 A017904 A017905 * A017907 A017908 A017909

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved