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A017904
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Expansion of 1/(1 - x^10 - x^11 - ...).
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12
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 20, 25, 31, 38, 46, 55, 65, 76, 89, 105, 125, 150, 181, 219, 265, 320, 385, 461, 550, 655, 780, 930, 1111, 1330, 1595, 1915, 2300, 2761, 3311, 3966, 4746, 5676
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OFFSET
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0,21
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COMMENTS
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A Lamé sequence of higher order.
a(n) = number of compositions of n in which each part is >=10. - Milan Janjic, Jun 28 2010
a(n+19) equals the number of binary words of length n having at least 9 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, 1).
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FORMULA
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For positive integers n and k such that k <= n <= 10*k, and 9 divides n-k, define c(n,k) = binomial(k,(n-k)/9), and c(n,k) = 0, otherwise. Then, for n>= 1, a(n+10) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011
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MAPLE
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f := proc(r) local t1, i; t1 := []; for i from 1 to r do t1 := [op(t1), 0]; od: for i from 1 to r+1 do t1 := [op(t1), 1]; od: for i from 2*r+2 to 50 do t1 := [op(t1), t1[i-1]+t1[i-1-r]]; od: t1; end; # set r = order
a:= n-> (Matrix(10, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0$8, 1][i] else 0 fi)^n)[10, 10]: 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, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]^n)[1, 1] \\ Charles R Greathouse IV, Oct 03 2016
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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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