

A017905


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


5



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
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OFFSET

0,23


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).


FORMULA

G.f.: (x1)/(x1+x^11).  Alois P. Heinz, Aug 04 2008
For positive integers n and k such that k <= n <= 11*k, and 10 divides nk, define c(n,k) = binomial(k,(nk)/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


MAPLE

a:= n> (Matrix(11, (i, j)> if (i=j1) 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 *)


PROG

(PARI) Vec((x1)/(x1+x^11)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012


CROSSREFS

Sequence in context: A246081 A117325 A180643 * A044962 A044824 A048310
Adjacent sequences: A017902 A017903 A017904 * A017906 A017907 A017908


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



