A025908 Expansion of 1/((1-x^7)*(1-x^8)*(1-x^9)).

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

Offset

0,17

Comments

Number of partitions of n into parts 7, 8, and 9. - Hoang Xuan Thanh, Sep 25 2025

Links

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

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

Formula

a(n) = floor((n^2+24*n-208)/1008 + ((5*n^2+n+3) mod 7)/7 + (4-(n mod 8))^2/16). - Hoang Xuan Thanh, Sep 25 2025

Mathematica

CoefficientList[Series[1/((1-x^7)(1-x^8)(1-x^9)), {x, 0, 120}], x] (* Harvey P. Dale, Jan 18 2015 *)

Prog

(PARI) a(n) = (n^2+24*n-208)/1008 + ((5*n^2+n+3)%7)/7 + (4-n%8)^2/16 -((7*n^2+6*n+2)%9)/9 \\ Hoang Xuan Thanh, Sep 25 2025

Crossrefs

Cf. A025907, A025909.

Sequence in context: A215029 A362832 A368751 * A134404 A334134 A249609

Adjacent sequences: A025905 A025906 A025907 * A025909 A025910 A025911

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved