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A017909 Expansion of 1/(1 - x^15 - x^16 - ...). 3
1, 0, 0, 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, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 21, 25, 30, 36, 43, 51, 60, 70, 81, 93, 106, 120, 135, 151, 169, 190, 215, 245, 281, 324, 375, 435, 505, 586, 679 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,31
COMMENTS
a(n+29) equals the number of binary words of length n having at least 14 zeros between every two successive ones. - Milan Janjic, Feb 09 2015
Number of compositions of n into parts >= 15. - Ilya Gutkovskiy, May 23 2017
LINKS
I. M. Gessel, Ji Li, Compositions and Fibonacci identities, J. Int. Seq. 16 (2013) 13.4.5
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
FORMULA
G.f.: (x-1)/(x-1+x^15). - Alois P. Heinz, Aug 04 2008
For positive integers n and k such that k <= n <= 15*k, and 14 divides n-k, define c(n,k) = binomial(k,(n-k)/14), and c(n,k) = 0, otherwise. Then, for n>=1, a(n+15) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011
MAPLE
a:= n -> (Matrix(15, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0$13, 1][i] else 0 fi)^n)[15, 15]: seq(a(n), n=0..80); # Alois P. Heinz, Aug 04 2008
MATHEMATICA
LinearRecurrence[{1, 0, 0, 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, 0, 0}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)
CoefficientList[Series[(x-1)/(x-1+x^15), {x, 0, 100}], x] (* Harvey P. Dale, Sep 04 2020 *)
PROG
(PARI) Vec((x-1)/(x-1+x^15)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
Sequence in context: A078510 A246100 A247250 * A345201 A316530 A296864
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified July 21 05:28 EDT 2024. Contains 374463 sequences. (Running on oeis4.)