A029312 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^9)*(1-x^12)).

1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 0, 3, 1, 1, 3, 2, 1, 4, 3, 1, 6, 3, 2, 7, 4, 3, 8, 6, 3, 10, 7, 4, 12, 8, 6, 14, 10, 7, 16, 12, 8, 19, 14, 10, 22, 16, 12, 25, 19, 14, 28, 22, 16, 32, 25, 19, 36, 28, 22, 40, 32, 25, 45, 36, 28

Offset

0,10

Comments

Number of partitions of n into parts 3, 7, 9, and 12. - Hoang Xuan Thanh, Apr 10 2026

Links

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

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

Formula

a(n) = floor((2*n^3+135*n^2+2700*n+16004)/27216 - (n mod 3)*(n^2+31*n+216)/648 - ((2*n^2+2*n) mod 3)*n*7/648 + ((4*n^3+4*n^2+3*n+4) mod 7)/7). - Hoang Xuan Thanh, Apr 10 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^9)(1-x^12)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 12 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^7)*(1-x^9)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 10 2026

Crossrefs

Sequence in context: A262114 A320780 A391984 * A287352 A391981 A243715

Adjacent sequences: A029309 A029310 A029311 * A029313 A029314 A029315

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved