A017877 Expansion of 1/(1 - x^9 - x^10).
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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1,1).
Crossrefs
Programs
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Magma
m:=80; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^9-x^10))); // Vincenzo Librandi, Jul 01 2013 -
Mathematica
CoefficientList[Series[1 / (1 - Total[x^Range[9, 10]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *) -
SageMath
def A017877_list(prec): P.
= PowerSeriesRing(ZZ, prec) return P( 1/(1-x^9-x^(10)) ).list() A017877_list(85) # G. C. Greubel, Sep 25 2024
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
Comments