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URL: https://oeis.org/A025890

⇱ A025890 - OEIS

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A025890
Expansion of 1/((1-x^5)*(1-x^8)*(1-x^12)).
6
1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 3, 2, 2, 2, 3, 3, 2, 2, 4, 3, 3, 2, 4, 4, 3, 3, 5, 4, 4, 3, 5, 5, 4, 4, 6, 5, 5, 4, 7, 6, 5, 5, 7, 7, 6, 5, 8, 7, 7, 6, 9, 8, 7, 7, 9, 9, 8, 7
OFFSET
0,21
COMMENTS
a(n) is the number of partitions of n into parts 5, 8, and 12. - Michel Marcus, Dec 12 2022
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,0,1,0,0,0,1,-1,0,0,0,-1,0,0,-1,0,0,0,0,1).
FORMULA
a(n) = floor(n*(75*n + 8*floor(n/4 + 1))/192) - floor((2*n^2-2)/5). - Hoang Xuan Thanh, Sep 21 2025
MATHEMATICA
CoefficientList[Series[1/((1-x^5)*(1-x^8)*(1-x^12)), {x, 0, 90}], x] (* G. C. Greubel, Dec 11 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 90); Coefficients(R!( 1/((1-x^5)*(1-x^8)*(1-x^12)) )); // G. C. Greubel, Dec 11 2022
(SageMath)
def A025890_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^5)*(1-x^8)*(1-x^12)) ).list()
A025890_list(90) # G. C. Greubel, Dec 11 2022
(PARI) a(n) = ((n+16)*(n+24) - 10*n*(n%4) + 192*((2*n^2+3)%5))\960 \\ Hoang Xuan Thanh, Sep 21 2025
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved