A029268 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^9)*(1-x^12)).

1, 0, 0, 1, 1, 0, 1, 1, 1, 2, 1, 1, 4, 2, 1, 4, 4, 2, 5, 4, 4, 7, 5, 4, 10, 7, 5, 11, 10, 7, 13, 11, 10, 16, 13, 11, 21, 16, 13, 23, 21, 16, 26, 23, 21, 31, 26, 23, 38, 31, 26, 41, 38, 31, 46, 41, 38, 53, 46, 41, 62, 53, 46, 67

Offset

0,10

Comments

Number of partitions of n into parts 3, 4, 9, and 12. - Vincenzo Librandi, Jun 03 2014

Links

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

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

Formula

a(n) = floor((n^3+54*n^2+756*n+8640)/7776 - (n mod 2)*n/96 - (n mod 3)*(n^2+28*n+216)/648 - ((2*n^2+2*n) mod 3)*n/162 + ((n^3+n^2+n+2) mod 4)*n/48). - Hoang Xuan Thanh, Mar 25 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^9) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^9)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A325528 A156861 A122773 * A347629 A176452 A244581

Adjacent sequences: A029265 A029266 A029267 * A029269 A029270 A029271

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved