A029320 Expansion of 1/((1-x^3)*(1-x^8)*(1-x^10)*(1-x^12)).

1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 3, 2, 3, 3, 3, 3, 5, 3, 4, 5, 5, 4, 7, 5, 7, 7, 7, 7, 10, 7, 9, 10, 11, 9, 13, 11, 13, 13, 14, 13, 18, 14, 17, 18, 19, 17, 22, 19, 23, 22, 24, 23, 29, 24, 28, 29, 31, 28, 35

Offset

0,13

Comments

Number of partitions of n into parts 3, 8, 10, and 12. - Hoang Xuan Thanh, Apr 14 2026

Links

Table of n, a(n) for n=0..66.

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

Formula

a(n) = floor((n^3+54*n^2+636*n+7040)/17280 - (n mod 2)*(n^2+33*n)/1920 + ((2*n^2+1) mod 3)*n/36 + ((n^2+n+2) mod 4)*n/192 + ((n+2) mod 3)*8/27 - ((2*n^2+n) mod 3)/9). - Hoang Xuan Thanh, Apr 14 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^8)(1-x^10)(1-x^12)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^8)*(1-x^10)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 14 2026

Crossrefs

Sequence in context: A133188 A261036 A008612 * A363992 A187450 A187449

Adjacent sequences: A029317 A029318 A029319 * A029321 A029322 A029323

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved