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A017877
Expansion of 1/(1 - x^9 - x^10).
15
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 1, 7, 21, 35, 35, 21, 7, 1, 0, 1, 8, 28, 56
OFFSET
0,20
COMMENTS
Number of compositions (ordered partitions) of n into parts 9 and 10. - Ilya Gutkovskiy, May 27 2017
FORMULA
a(n) = a(n-9) + a(n-10) for n > 9. - Vincenzo Librandi, Jul 01 2013
a(n) = Sum_{k=0..floor(n/9)} binomial(k,n-9*k). - Seiichi Manyama, Oct 01 2024
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[9, 10]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
PROG
(Magma)
m:=80; R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^9-x^10))); // Vincenzo Librandi, Jul 01 2013
(SageMath)
def A017877_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x^9-x^(10)) ).list()
A017877_list(85) # G. C. Greubel, Sep 25 2024
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved