A025891 Expansion of 1/((1-x^5)*(1-x^9)*(1-x^10)).

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 1, 2, 3, 0, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 6, 2, 3, 4, 5, 7, 2, 3, 4, 6, 8, 3, 4, 5, 7, 9, 3, 4, 6, 8, 10, 4, 5, 7, 9, 11, 4, 6, 8, 10, 12, 5, 7, 9

Offset

0,11

Comments

a(n) is the number of partitions of n into parts 5, 9, and 10. - Michel Marcus, Dec 12 2022

Links

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

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

Formula

a(n) = floor((n^2-12*n+140)/900 + (n+5)*((n+4) mod 5)/50 + ((8*n^2+3*n+4) mod 9)/9). - Hoang Xuan Thanh, Sep 21 2025

Mathematica

CoefficientList[Series[1/((1-x^5)(1-x^9)(1-x^10)), {x, 0, 80}], x] (* Harvey P. Dale, Mar 05 2019 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 90); Coefficients(R!( 1/((1-x^5)*(1-x^9)*(1-x^10)) )); // G. C. Greubel, Dec 11 2022
(SageMath)
def A025891_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^5)*(1-x^9)*(1-x^10)) ).list()
A025891_list(90) # G. C. Greubel, Dec 11 2022

Crossrefs

Sequence in context: A079126 A339086 A186336 * A341000 A120630 A248509

Adjacent sequences: A025888 A025889 A025890 * A025892 A025893 A025894

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved