A029161 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^8)*(1-x^9)).

1, 0, 1, 1, 1, 1, 2, 1, 3, 3, 3, 4, 5, 4, 6, 6, 7, 8, 10, 9, 12, 12, 13, 14, 17, 16, 20, 21, 22, 24, 27, 26, 31, 32, 34, 37, 41, 40, 46, 47, 50, 53, 58, 58, 65, 67, 70, 74, 80, 80, 88, 91, 95, 100, 107, 107, 117, 120, 125

Offset

0,7

Comments

a(n) is the number of partitions of n into parts 2, 3, 8, and 9. - Hoang Xuan Thanh, Oct 06 2025

Links

Table of n, a(n) for n=0..58.

Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1,0,0,1,1,-1,-2,-1,1,1,0,0,-1,0,1,1,0,-1).

Formula

floor((n^3+33*n^2+300*n+1120)/2592 - (n+5)*(n mod 2)/32 + n*((n^2+n+1) mod 3)/27 + ((n+2) mod 3)/3). - Hoang Xuan Thanh, Oct 06 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^8)(1-x^9)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 18 2020 *)
LinearRecurrence[{0, 1, 1, 0, -1, 0, 0, 1, 1, -1, -2, -1, 1, 1, 0, 0, -1, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 1, 2, 1, 3, 3, 3, 4, 5, 4, 6, 6, 7, 8, 10, 9, 12, 12}, 60] (* Harvey P. Dale, Jul 21 2024 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^8)*(1-x^9))+O(x^60)) \\ Hoang Xuan Thanh, Oct 06 2025

Crossrefs

Sequence in context: A110425 A174257 A105637 * A035384 A360033 A303974

Adjacent sequences: A029158 A029159 A029160 * A029162 A029163 A029164

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved