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URL: https://oeis.org/A025893

⇱ A025893 - OEIS

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A025893
Expansion of 1/((1-x^5)*(1-x^9)*(1-x^12)).
5
1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 4, 3, 3, 4, 3, 4, 4, 3, 4, 5, 4, 4, 5, 4, 5, 6, 4, 5, 6, 5, 6, 6, 5, 6, 7, 6, 6, 8, 6, 7, 8, 6, 8, 8, 7, 8, 9, 8, 8, 10, 8, 9, 10, 8, 10
OFFSET
0,25
COMMENTS
a(n) is the number of partitions of n into parts 5, 9, and 12. - Joerg Arndt, Jan 17 2024
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,0,0,1,0,0,1,0,-1,0,0,-1,0,0,0,-1,0,0,0,0,1).
FORMULA
a(n) = floor((5*n*(35*n+38) - 6*(n+5)*floor((n+2)/3))/216) - floor((4*n^2+4*n-3)/5). - Hoang Xuan Thanh, Sep 21 2025
MATHEMATICA
CoefficientList[Series[1/((1-x^5)(1-x^9)(1-x^12)), {x, 0, 90}], x] (* Harvey P. Dale, Jan 09 2017 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^5)*(1-x^9)*(1-x^12)) )); // G. C. Greubel, Jan 16 2024
(SageMath)
def A025893_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( 1/((1-x^5)*(1-x^9)*(1-x^12)) ).list()
A025893_list(100) # G. C. Greubel, Jan 16 2024
(PARI) Vec(1/((1-x^5)*(1-x^9)*(1-x^12))+O(x^90)) \\ Stefano Spezia, Sep 16 2025
(PARI) a(n) = ((n^2+16*n+548 + 10*(n+5)*((n+2)%3))/1080 + ((4*n^2+4*n+2)%5)/5)\1 \\ Hoang Xuan Thanh, Sep 21 2025
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved