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A017888
Expansion of 1/(1 - x^10 - x^11 - x^12).
3
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 1, 4, 10, 16, 19, 16, 10, 4, 1, 0, 1, 5, 15, 30, 45, 51, 45, 30, 15, 5, 2, 6, 21, 50, 90, 126, 141, 126, 90, 50
OFFSET
0,22
COMMENTS
Number of compositions (ordered partitions) of n into parts 10, 11 and 12. - Ilya Gutkovskiy, May 27 2017
LINKS
FORMULA
a(n) = a(n-10) + a(n-11) + a(n-12), for n > 11. - Vincenzo Librandi, Jul 01 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[10, 12]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
PROG
(Magma)
m:=80; R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!(1/(1-x^10-x^11-x^12))); // Vincenzo Librandi, Jul 01 2013
(PARI)
my(x='x+O('x^80)); Vec(1/(1-x^10-x^11-x^12)) \\ Altug Alkan, Oct 04 2018
(SageMath)
def A017888_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-x)/(1-x-x^10+x^(13)) ).list()
A017888_list(80) # G. C. Greubel, Sep 25 2024
KEYWORD
nonn,easy
STATUS
approved