A029323 Expansion of 1/((1-x^3)*(1-x^9)*(1-x^10)*(1-x^12)).

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 3, 1, 0, 3, 1, 0, 4, 2, 1, 5, 3, 1, 6, 3, 1, 7, 4, 2, 9, 5, 3, 10, 6, 3, 12, 7, 4, 14, 9, 5, 16, 10, 6, 18, 12, 7, 21, 14, 9, 23, 16, 10, 26, 18, 12, 29, 21, 14, 33, 23, 16, 36, 26, 18, 40, 29, 21, 44, 33, 23, 49, 36, 26, 53

Offset

0,10

Comments

Number of partitions of n into parts 3, 9, 10, and 12. - Hoang Xuan Thanh, Apr 15 2026

Links

Table of n, a(n) for n=0..75.

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

Formula

a(n) = floor((n^3+81*n^2+1944*n+11400)/19440 - (n mod 2)*n/240 - (n mod 3)*(3*n^2+102*n+214)/1944 - ((2*n^2+2*n) mod 3)*n*5/324 + ((2*n^2+1) mod 3)*85/162). - Hoang Xuan Thanh, Apr 15 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^9)(1-x^10)(1-x^12)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^9)*(1-x^10)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 15 2026

Crossrefs

Sequence in context: A280494 A168016 A342301 * A194849 A071802 A110355

Adjacent sequences: A029320 A029321 A029322 * A029324 A029325 A029326

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved