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URL: https://oeis.org/A017905

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A017905
Expansion of 1/(1 - x^11 - x^12 - ...).
6
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
0,23
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
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
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
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 *)
PROG
(PARI) Vec((x-1)/(x-1+x^11)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
Sequence in context: A246081 A117325 A180643 * A333598 A044962 A044824
KEYWORD
nonn,easy
STATUS
approved