A029223 Expansion of 1/((1-x^2)*(1-x^6)*(1-x^9)*(1-x^12)).

1, 0, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 4, 1, 4, 2, 4, 2, 7, 2, 7, 4, 7, 4, 11, 4, 11, 7, 11, 7, 16, 7, 16, 11, 16, 11, 23, 11, 23, 16, 23, 16, 31, 16, 31, 23, 31, 23, 41, 23, 41, 31, 41, 31, 53, 31, 53, 41, 53, 41, 67, 41, 67, 53

Offset

0,7

Comments

Number of partitions of n into parts 2, 6, 9, and 12. - Joerg Arndt, Jun 02 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((n^3+51*n^2+774*n+7776 - 27*(n^2+29*n+72)*(n mod 2) + 6*(n^2+29*n)*((n+2) mod 3) + n*(12+54*(-1)^floor(n/3))*((n+1)^2 mod 3))/7776). - Hoang Xuan Thanh, Oct 23 2025

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^6) (1 - x^9) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 02 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^6)*(1-x^9)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

Crossrefs

Sequence in context: A025814 A029354 A035434 * A305576 A129679 A319514

Adjacent sequences: A029220 A029221 A029222 * A029224 A029225 A029226

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved