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A017907
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Expansion of 1/(1 - x^13 - x^14 - ...).
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4
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 19, 23, 28, 34, 41, 49, 58, 68, 79, 91, 104, 118, 134, 153, 176, 204, 238, 279, 328, 386, 454, 533, 624, 728, 846, 980, 1133, 1309
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OFFSET
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0,27
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COMMENTS
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a(n) = number of compositions of n in which each part is >= 13. - Milan Janjic, Jun 28 2010
a(n+25) equals the number of binary words of length n having at least 12 zeros between every two successive ones. - Milan Janjic, Feb 09 2015
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
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FORMULA
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For positive integers n and k such that k <= n <= 13*k, and 12 divides n-k, define c(n,k) = binomial(k,(n-k)/12), and c(n,k) = 0, otherwise. Then, for n>=1, a(n+13) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011
a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=0, a(10)=0, a(11)=0, a(12)=0, a(n)=a(n-1)+a(n-13). - Harvey P. Dale, Feb 07 2015
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MAPLE
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a:= n-> (Matrix(13, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0$11, 1][i] else 0 fi)^n)[13, 13]: seq(a(n), n=0..80); # Alois P. Heinz, Aug 04 2008
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 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^13), {x, 0, 70}], x] (* Harvey P. Dale, Feb 07 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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