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A025895

Expansion of 1/((1-x^5)*(1-x^10)*(1-x^12)).

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 1, 0, 0, 3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 4, 0, 3, 0, 2, 4, 1, 3, 0, 2, 5, 1, 4, 0, 3, 5, 2, 4, 1, 3, 6, 2, 5, 1, 4, 6, 3, 5, 2, 4, 8, 3, 6, 2, 5, 8, 4, 6, 3, 5, 10, 4, 8, 3, 6, 10, 5, 8, 4, 6

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,11

COMMENTS

a(n) is the number of partitions of n into parts 5, 10, and 12. - Joerg Arndt, Jan 17 2024

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,0,0,0,1,0,1,0,0,-1,0,-1,0,0,0,0,-1,0,0,0,0,1).

FORMULA

a(n) = floor((n^2 - 21*n + 75 + 5*(n+18)*(-1)^n + 24*n*((2*n+4) mod 5) + ((-1)^(n mod 5)*(17 - 5*(n mod 5)) - 5*((n mod 5) mod 2) + 21)^2)/1200). - Hoang Xuan Thanh, Sep 23 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^5)(1-x^10)(1-x^12)), {x, 0, 100}], x] (* Harvey P. Dale, Mar 30 2011 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Integers(), 120); Coefficients(R!( 1/((1-x^5)*(1-x^10)*(1-x^12)) )); // G. C. Greubel, Jan 17 2024

(SageMath)

def A025895_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( 1/((1-x^5)*(1-x^10)*(1-x^12)) ).list()

A025895_list(120) # G. C. Greubel, Jan 17 2024

(PARI) a(n) = (n^2-21*n+75 + 5*(n+18)*(-1)^n + 24*n*((2*n+4)%5) + ([38, 4, 28, 14, 18][n%5+1])^2)\1200 \\ Hoang Xuan Thanh, Sep 23 2025

CROSSREFS

Cf. A025893, A025894, A025896.