A029358 Expansion of 1/((1-x^4)*(1-x^6)*(1-x^11)*(1-x^12)).

1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 3, 0, 1, 1, 3, 1, 3, 1, 3, 1, 4, 3, 6, 1, 4, 3, 7, 3, 7, 3, 7, 4, 9, 6, 11, 4, 9, 7, 13, 7, 13, 7, 14, 9, 16, 11, 19, 9, 17, 13, 22, 13, 22, 14, 24, 16, 26, 19, 30, 17, 28, 22, 34, 22, 35, 24, 37

Offset

0,13

Comments

Number of partitions of n into parts 4, 6, 11, and 12. - Hoang Xuan Thanh, May 14 2026

Links

Table of n, a(n) for n=0..68.

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

Formula

a(n) = floor((n+32)*(n^2+34*n-92)/19008 - (n mod 2)*(n+1)*(n+32)/576 + ((2*n^2+1) mod 3)*n/72 + ((n^2+n+2) mod 4)*n/96 + (((n+5) mod 6) - ((n+3) mod 6) - ((n+2) mod 6) + (n mod 6))*n/432 + (4*((n+3) mod 4) + ((n+1) mod 4) - (n mod 4))/16 + ((10*n^3+5*n+4) mod 11)/11). - Hoang Xuan Thanh, May 14 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^6)(1-x^11)(1-x^12)), {x, 0, 70}], x] (* Harvey P. Dale, Dec 09 2011 *)

Prog

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

Crossrefs

Sequence in context: A341411 A174433 A174624 * A088512 A396228 A094921

Adjacent sequences: A029355 A029356 A029357 * A029359 A029360 A029361

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved