A017905 Expansion of 1/(1 - x^11 - x^12 - ...).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 21, 26, 32, 39, 47, 56, 66, 77, 89, 103, 120, 141, 167, 199, 238, 285, 341, 407, 484, 573, 676, 796, 937, 1104, 1303, 1541, 1826, 2167, 2574, 3058

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) = number of compositions of n in which each part is >= 11. - Milan Janjic, Jun 28 2010

a(n+21) equals the number of binary words of length n having at least 10 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, 1).

Programs

Maple

a:= n-> (Matrix(11, (i,j)-> if (i=j-1) then 1 elif j=1 then [1, 0$9, 1][i] else 0 fi)^n)[11,11]: seq(a(n), n=0..70); # Alois P. Heinz, Aug 04 2008

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)

PARI

Vec((x-1)/(x-1+x^11)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

G.f.: (x-1)/(x-1+x^11). - Alois P. Heinz, Aug 04 2008

For positive integers n and k such that k <= n <= 11*k, and 10 divides n-k, define c(n,k) = binomial(k,(n-k)/10), and c(n,k) = 0, otherwise. Then, for n>=1, a(n+11) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011