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A017880
Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13).
10
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 3, 6, 10, 15, 18, 19, 18, 15, 11, 10, 13, 21, 35, 52, 68, 80, 85, 81, 73, 67, 70, 90, 131, 189, 256, 320, 366, 387, 386, 376, 381, 431, 547
OFFSET
0,20
COMMENTS
Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12 and 13. - Ilya Gutkovskiy, May 27 2017
LINKS
FORMULA
a(n) = a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - Vincenzo Librandi, Jul 01 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[9, 13]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}, 70] (* Harvey P. Dale, Apr 03 2018 *)
PROG
(Magma)
m:=70; R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13))); // Vincenzo Librandi, Jul 01 2013
(SageMath)
def A017880_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-x)/(1-x-x^9+x^(14)) ).list()
A017880_list(80) # G. C. Greubel, Sep 25 2024
KEYWORD
nonn,easy
STATUS
approved