A029316 Expansion of 1/((1-x^3)*(1-x^8)*(1-x^9)*(1-x^10)).

1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 4, 3, 3, 4, 3, 3, 5, 4, 5, 7, 6, 6, 8, 6, 7, 9, 8, 9, 12, 10, 11, 13, 12, 12, 15, 14, 15, 18, 17, 17, 21, 19, 20, 23, 22, 23, 27, 25, 27, 30, 29, 30, 34, 32, 34, 38, 37, 38

Offset

0,10

Comments

Number of partitions of n into parts 3, 8, 9, and 10. - Hoang Xuan Thanh, Apr 12 2026

Links

Table of n, a(n) for n=0..65.

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

Formula

a(n) = floor((n^3+45*n^2-948*n+9727)/12960 - (n mod 2)*n/160 + ((2*n^2+1) mod 3)*(n+15)/27 - ((n+1) mod 3)/81 + (floor(n/9) + floor((n+1)/9) + floor((n+2)/9))/3). - Hoang Xuan Thanh, Apr 12 2026

Prog

(PARI) Vec(1/((1-x^3)*(1-x^8)*(1-x^9)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A161069 A161108 A161043 * A104368 A218878 A364137

Adjacent sequences: A029313 A029314 A029315 * A029317 A029318 A029319

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved