A029304 Expansion of 1/((1-x^3)*(1-x^6)*(1-x^10)*(1-x^12)).

1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 4, 1, 0, 4, 2, 0, 6, 2, 1, 6, 4, 1, 9, 4, 2, 9, 6, 2, 13, 6, 4, 13, 9, 4, 18, 9, 6, 18, 13, 6, 24, 13, 9, 24, 18, 9, 31, 18, 13, 31, 24, 13, 39, 24, 18, 39, 31, 18, 49, 31, 24, 49, 39, 24, 60

Offset

0,7

Comments

Number of partitions of n into parts 3, 6, 10, and 12. - Hoang Xuan Thanh, Apr 08 2026

Links

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

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

Formula

a(n) = floor((n^3+81*n^2+1818*n+6912)/12960 - (3*(n mod 2) + 10*(n mod 3))*(n^2+31*n)/4320 - ((2*n^2+2*n) mod 3)*n*5/216 + (n/144)*(1-(n mod 3))*(-1)^floor(n/3) + ((n^2+2) mod 3)/3). - Hoang Xuan Thanh, Apr 08 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^10)(1-x^12)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^6)*(1-x^10)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 08 2026

Crossrefs

Sequence in context: A035437 A339815 A156996 * A030202 A159818 A379944

Adjacent sequences: A029301 A029302 A029303 * A029305 A029306 A029307

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved