A029321 Expansion of 1/((1-x^3)*(1-x^8)*(1-x^11)*(1-x^12)).

1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 2, 2, 0, 2, 2, 1, 2, 2, 2, 3, 2, 3, 4, 4, 3, 4, 5, 4, 4, 6, 5, 6, 7, 6, 8, 9, 6, 9, 10, 8, 10, 11, 10, 13, 12, 12, 15, 15, 13, 16, 17, 16, 17, 19, 19, 21, 21, 21, 24, 25, 22, 26, 28, 26, 28, 31, 30

Offset

0,12

Comments

Number of partitions of n into parts 3, 8, 11, and 12. - Hoang Xuan Thanh, Apr 15 2026

Links

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

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

Formula

a(n) = floor((n^3+51*n^2+1107*n-4784)/19008 - (n mod 2)*n/64 - ((2*n^2+2*n) mod 3)*n/36 + ((n mod 4) - ((n+1) mod 4))*n/192 + ((n+2) mod 3)/3 + ((10*n^3+4*n^2+4*n+10) mod 11)/11). - Hoang Xuan Thanh, Apr 15 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^8)(1-x^11)(1-x^12)), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 2, 2, 0, 2, 2, 1, 2, 2, 2, 3, 2, 3, 4, 4, 3, 4, 5, 4, 4, 6, 5, 6, 7}, 70] (* Harvey P. Dale, Jul 31 2017 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^8)*(1-x^11)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 15 2026

Crossrefs

Sequence in context: A218491 A111165 A349812 * A029310 A348220 A134131

Adjacent sequences: A029318 A029319 A029320 * A029322 A029323 A029324

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved