A025924 Expansion of 1/((1-x^9)*(1-x^10)*(1-x^12)).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 0, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 2, 3, 3, 2, 4, 2, 2, 3, 3, 2, 4, 3, 3, 4, 4, 2, 5, 3, 3, 4, 4, 3, 5, 4

Offset

0,31

Comments

Number of partitions of n into parts 9, 10, and 12. - Hoang Xuan Thanh, Sep 29 2025

Links

Table of n, a(n) for n=0..79.

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

Formula

a(n)= +a(n-9) +a(n-10) +a(n-12) -a(n-19) -a(n-21) -a(n-22) +a(n-31). - R. J. Mathar, Jul 19 2014

a(n) = floor((n^2+60*n+864)/2160 - n*(n mod 2)/120 - n*(n mod 3)/108 + ((2*n^2+3 + (4*n+2)*(n mod 2)) mod 5)/5). - Hoang Xuan Thanh, Sep 29 2025

Mathematica

CoefficientList[Series[1/((1-x^9)(1-x^10)(1-x^12)), {x, 0, 90}], x] (* or *) LinearRecurrence[ {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 2}, 90] (* Harvey P. Dale, Jun 19 2022 *)

Prog

(PARI) Vec(1/((1-x^9)*(1-x^10)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Sep 29 2025

Crossrefs

Sequence in context: A225192 A262432 A135694 * A025904 A137993 A353329

Adjacent sequences: A025921 A025922 A025923 * A025925 A025926 A025927

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved