A029288 Expansion of 1/((1-x^3)*(1-x^5)*(1-x^9)*(1-x^12)).

1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 3, 1, 2, 4, 1, 3, 5, 2, 4, 6, 3, 5, 8, 4, 6, 10, 5, 8, 12, 6, 10, 14, 8, 12, 17, 10, 14, 20, 12, 17, 23, 14, 20, 27, 17, 23, 31, 20, 27, 35, 23, 31, 40, 27, 35, 45, 31, 40, 51, 35, 45, 57, 40, 51, 63, 45, 57, 70, 51, 63, 78, 57

Offset

0,10

Comments

Number of partitions of n into parts 3, 5, 9, and 12. - Vincenzo Librandi, Jun 04 2014

Links

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

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

Formula

a(n) = floor((2*n^3+57*n^2+312*n+844)/19440 + ((n+2) mod 3)*(n^2+29*n+216)/648 - ((2*n^2+n) mod 3)*n*5/648 + ((n^3+n^2+n+2) mod 5)/5). - Hoang Xuan Thanh, Mar 31 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^5) (1 - x^9) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 04 2014 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^5)*(1-x^9)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A374921 A187846 A181087 * A238899 A187207 A382501

Adjacent sequences: A029285 A029286 A029287 * A029289 A029290 A029291

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved