A029356 Expansion of 1/((1-x^4)*(1-x^6)*(1-x^9)*(1-x^12)).

1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 3, 1, 1, 1, 3, 1, 4, 1, 3, 3, 4, 1, 7, 3, 4, 4, 7, 3, 9, 4, 7, 7, 9, 4, 14, 7, 9, 9, 14, 7, 17, 9, 14, 14, 17, 9, 24, 14, 17, 17, 24, 14, 29, 17, 24, 24, 29, 17, 38, 24, 29, 29, 38, 24, 45, 29

Offset

0,13

Comments

Number of partitions of n into parts 4, 6, 9, and 12. - Hoang Xuan Thanh, May 13 2026

Links

Table of n, a(n) for n=0..67.

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

Formula

a(n) = floor((n+50)*(n^2+22*n+304)/15552 - (n mod 2)*(n+15)*(n+16)/576 - (n mod 3)*(n+10)*(n+30)/1296 - ((2*n^2+2*n) mod 3)*n/324 + (((n+1)*(n+2)) mod 4)*(n+3)/96 + ((n mod 6) + ((n+3) mod 6) - ((n+1) mod 6) - ((n+2) mod 6))*n/432). - Hoang Xuan Thanh, May 13 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^6)(1-x^9)(1-x^12)), {x, 0, 70}], x] (* Harvey P. Dale, Mar 09 2013 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^6)*(1-x^9)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A183093 A183096 A377071 * A334019 A291448 A114006

Adjacent sequences: A029353 A029354 A029355 * A029357 A029358 A029359

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved