A025892 Expansion of 1/((1-x^5)*(1-x^9)*(1-x^11)).

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

Offset

0,21

Comments

Number of partitions of n into parts 5, 9, and 11. - Hoang Xuan Thanh, Sep 21 2025

Links

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

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

Formula

a(n) = floor((19*n^2+7*n)/18) - floor((3*n^2-2)/5) - floor((5*n^2+4*n+5)/11). - Hoang Xuan Thanh, Sep 21 2025

Mathematica

CoefficientList[Series[1/((1-x^5)(1-x^9)(1-x^11)), {x, 0, 80}], x] (* Harvey P. Dale, Nov 06 2017 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^5)*(1-x^9)*(1-x^11)) )); // G. C. Greubel, Jan 16 2024
(SageMath)
def A025892_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^5)*(1-x^9)*(1-x^11)) ).list()
A025892_list(80) # G. C. Greubel, Jan 16 2024
(PARI) Vec(1/((1-x^5)*(1-x^9)*(1-x^11))+O(x^99)) \\ Joerg Arndt, Jan 16 2024
(PARI) a(n) = (19*n^2+7*n)\18 - (3*n^2-2)\5 - (5*n^2+4*n+5)\11 \\ Hoang Xuan Thanh, Sep 21 2025

Crossrefs

Cf. A025890, A025891, A025893, A025894.

Sequence in context: A102005 A051700 A337006 * A025883 A111335 A345238

Adjacent sequences: A025889 A025890 A025891 * A025893 A025894 A025895

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved