A029389 Expansion of 1/((1-x^5)*(1-x^6)*(1-x^9)*(1-x^12)).

1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0, 1, 2, 1, 2, 3, 1, 2, 3, 2, 3, 5, 2, 3, 5, 3, 5, 7, 3, 5, 7, 5, 7, 10, 5, 7, 10, 7, 10, 13, 7, 10, 14, 10, 13, 17, 10, 14, 18, 13, 17, 22, 14, 18, 23, 17, 22, 28, 18, 23, 29, 22, 28, 34, 23

Offset

0,13

Comments

Number of partitions of n into parts 5, 6, 9, and 12. - Hoang Xuan Thanh, Jul 12 2026

Links

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

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

Formula

a(n) = floor((n^3+33*n^2+284*n+11664)/19440 - (n mod 2)*(n+41)/144 + ((n+2) mod 3)*(n^2+32*n)/1296 + (((n+1) mod 3) - (n mod 3))*(16-27*(n mod 2))*n/1944 + ((3*n^3+4*n^2+2*n+2) mod 5)/5). - Hoang Xuan Thanh, Jul 12 2026

Mathematica

CoefficientList[Series[1/((1-x^5)(1-x^6)(1-x^9)(1-x^12)), {x, 0, 70}], x] (* Harvey P. Dale, May 06 2018 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 0, 0, 1, 1, 0, 0, 1, 0, -1, 1, 0, -1, -1, 0, -1, -1, 0, 1, -1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0, 1, 2, 1, 2, 3, 1, 2, 3, 2, 3, 5, 2, 3, 5, 3, 5, 7, 3}, 70] (* Harvey P. Dale, May 06 2018 *)

Prog

(PARI) Vec(1/((1-x^5)*(1-x^6)*(1-x^9)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Feb 28 2020

Crossrefs

Sequence in context: A247918 A237203 A339444 * A025835 A029277 A077905

Adjacent sequences: A029386 A029387 A029388 * A029390 A029391 A029392

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved