A025904 - OEIS

A025904

Expansion of 1/((1-x^6)*(1-x^9)*(1-x^10)).

1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 1, 4, 2, 2, 3, 3, 1, 4, 2, 2, 4, 4, 2, 5, 3, 3, 4, 4, 2, 6, 4, 4, 5, 5, 3, 7, 4, 4, 6, 6, 4, 8, 5, 5, 7, 7, 4, 9, 6, 6, 8, 8, 5, 10, 7

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OFFSET

0,19

COMMENTS

a(n) is the number of partitions of n into parts 6, 9, and 10. - Michel Marcus, Jan 24 2024

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) = floor((n^2+45*n+972)/1080 + (n+12)*(-1)^n/120 - (n+12)*(n mod 3)/54). - Hoang Xuan Thanh, Sep 25 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^6)(1-x^9)(1-x^10)), {x, 0, 80}], x] (* Harvey P. Dale, Jun 09 2019 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^9)*(1-x^10)) )); // G. C. Greubel, Jan 23 2024

(SageMath)

def A025904_list(prec):

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

return P( 1/((1-x^6)*(1-x^9)*(1-x^10)) ).list()

A025904_list(100) # G. C. Greubel, Jan 23 2024

(PARI) a(n) = (n^2+45*n+972 + 9*(n+12)*(-1)^n - 20*(n+12)*(n%3))\1080 \\ Hoang Xuan Thanh, Sep 25 2025

CROSSREFS

Cf. A025902, A025903, A025905, A025906.

Sequence in context: A262432 A135694 A025924 * A137993 A353329 A282778

Adjacent sequences: A025901 A025902 A025903 * A025905 A025906 A025907

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved