A029155 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^12)).

1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 3, 3, 7, 3, 7, 7, 7, 7, 13, 7, 13, 13, 13, 13, 22, 13, 22, 22, 22, 22, 34, 22, 34, 34, 34, 34, 50, 34, 50, 50, 50, 50, 70, 50, 70, 70, 70, 70, 95, 70, 95, 95, 95, 95, 125, 95, 125, 125, 125, 125

Offset

0,7

Comments

a(n) is the number of partitions of n into parts 2, 3, 6, and 12. - Hoang Xuan Thanh, Oct 04 2025

Links

Table of n, a(n) for n=0..59.

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

Formula

a(n) = floor((n^3+33*n^2+318*n+2592)/2592 + n*(n+21)*((n+2) mod 3)/432 - (n^2+23*n+18)*(n mod 2)/288 + (-1)^(floor(n/3))*n*((n+1)^2 mod 3)/144 + n*((2*n^2+1) mod 3)/108). - Hoang Xuan Thanh, Oct 04 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^6)(1-x^12)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 18 2020 *)
LinearRecurrence[{0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 3, 3, 7, 3, 7, 7, 7, 7, 13, 7, 13, 13, 13}, 60] (* Harvey P. Dale, Jul 18 2023 *)

Prog

(PARI) my(x='x+O('x^60)); Vec(1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^12))) \\ Joerg Arndt, Oct 04 2025

Crossrefs

Sequence in context: A334070 A025796 A024163 * A042951 A194299 A029154

Adjacent sequences: A029152 A029153 A029154 * A029156 A029157 A029158

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved