A025878 - OEIS

A025878

Expansion of 1/((1-x^5)*(1-x^6)*(1-x^9)).

1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 3, 2, 2, 3, 2, 3, 4, 2, 3, 4, 3, 4, 5, 3, 4, 5, 4, 5, 6, 4, 5, 7, 5, 6, 7, 5, 7, 8, 6, 7, 9, 7, 8, 9, 7, 9, 11, 8, 9, 11, 9, 11, 12, 9, 11, 13, 11, 12, 14, 11, 13, 15, 12, 14, 16, 13, 15

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

OFFSET

0,16

COMMENTS

Number of partitions of n into parts 5, 6, and 9. - Hoang Xuan Thanh, Sep 15 2025

LINKS

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

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

FORMULA

a(n) = floor((n^2+10*n+96)/540 + (n+6)*((n+2) mod 3)/54 + ((3*n^2+3) mod 5)/5). - Hoang Xuan Thanh, Sep 15 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^5)(1-x^6)(1-x^9)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 1, 1, 0, 0, 1, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 2, 1}, 100] (* Harvey P. Dale, Jul 29 2021 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Rationals(), 80); Coefficients(R!( 1/((1-x^5)*(1-x^6)*(1-x^9)) )); // G. C. Greubel, Nov 17 2022

(SageMath)

def A025878_list(prec):

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

return P( 1/((1-x^5)*(1-x^6)*(1-x^9)) ).list()

A025878_list(80) # G. C. Greubel, Nov 17 2022

CROSSREFS

Cf. A025876, A025877, A025879, A025880, A025881.

Sequence in context: A008676 A025893 A296977 * A143421 A137672 A141272

Adjacent sequences: A025875 A025876 A025877 * A025879 A025880 A025881

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved