A025850 Expansion of 1/((1-x^3)*(1-x^8)*(1-x^9)).

1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 4, 2, 3, 5, 2, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 10, 6, 8, 11, 7, 9, 12, 7, 10, 13, 8, 11, 14, 9, 12, 15, 10, 13, 16, 11, 14, 17, 12, 15, 19

Offset

0,10

Comments

Number of partitions of n into parts 3, 8, and 9. - Hoang Xuan Thanh, Sep 06 2025

Links

Table of n, a(n) for n=0..72.

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

Formula

a(n) = floor((n^2 + 4*n + 233)/432 + (n+2)*((n+2) mod 3)/27 + (((n+4) mod 8) - ((n+5) mod 8) + ((n+6) mod 8) - ((n+7) mod 8) + ((5*n^2 + 4*n + 7) mod 8))/16). - Hoang Xuan Thanh, Sep 06 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^8)(1-x^9)), {x, 0, 80}], x] (* Harvey P. Dale, Jul 19 2011 *)

Prog

(PARI) a(n) = (n^2 + 20*n + 211)/432 + (n+2)*[1, -1, 0][n%3+1]/27 + [7, 8, 3, 8, 7, 0, 3, 0][n%8+1]/16 - [0, 25, 21, 9, 25, 21, 9, 16, 12][n%9+1]/27 \\ Hoang Xuan Thanh, Sep 06 2025

Crossrefs

Sequence in context: A394020 A215590 A097203 * A096771 A129714 A022333

Adjacent sequences: A025847 A025848 A025849 * A025851 A025852 A025853

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved