A025920 - OEIS

A025920

Expansion of 1/((1-x^8)*(1-x^9)*(1-x^12)).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 2, 1, 3, 3, 1, 1, 4, 2, 2, 2, 3, 3, 3, 1, 4, 4, 2, 2, 5, 3, 3, 3, 4, 4, 4, 2, 5, 5, 3, 3, 7, 4, 4, 4, 5, 5, 5, 3

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

OFFSET

0,25

COMMENTS

Number of partitions of n into parts 8, 9, and 12. - Hoang Xuan Thanh, Sep 28 2025

LINKS

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

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

FORMULA

a(n) = a(n-8) + a(n-9) + a(n-12) - a(n-17) - a(n-20) - a(n-21) + a(n-29). - R. J. Mathar, Jul 19 2014

a(n) = floor((n^2+40*n+1408)/1728 + (n+10)*(((n+2) mod 3)/108 - (n mod 4)/96)). - Hoang Xuan Thanh, Sep 28 2025

PROG

(PARI) a(n) = (n^2+40*n+1408 + (n+10)*(16*((n+2)%3) - 18*(n%4)))\1728 \\ Hoang Xuan Thanh, Sep 28 2025

CROSSREFS

Sequence in context: A144435 A182533 A173120 * A037821 A316863 A037911

Adjacent sequences: A025917 A025918 A025919 * A025921 A025922 A025923

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved