A029317 Expansion of 1/((1-x^3)*(1-x^8)*(1-x^9)*(1-x^11)).

1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 2, 1, 3, 3, 2, 4, 3, 3, 4, 4, 4, 5, 6, 5, 6, 7, 6, 7, 9, 7, 9, 11, 8, 11, 12, 10, 13, 14, 12, 16, 16, 14, 18, 18, 17, 20, 21, 20, 23, 24, 23, 26, 27, 26, 29, 31, 29, 33, 35, 33, 37, 39

Offset

0,10

Comments

Number of partitions of n into parts 3, 8, 9, and 11. - Hoang Xuan Thanh, Apr 12 2026

Links

Table of n, a(n) for n=0..66.

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

Formula

a(n) = floor((2*n^3+93*n^2+1656*n-2864)/28512 - ((2*n^2+2*n) mod 3)*(n+6)/27 + ((n+2) mod 3)*28/81 + ((6*n^3+4*n^2+7*n+10) mod 11)/11). - Hoang Xuan Thanh, Apr 12 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^8)(1-x^9)(1-x^11)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 12 2020 *)
LinearRecurrence[{0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 2, 1, 3, 3, 2, 4, 3, 3, 4, 4, 4, 5, 6, 5, 6, 7}, 70] (* Harvey P. Dale, Nov 28 2023 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^8)*(1-x^9)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 12 2026

Crossrefs

Sequence in context: A031358 A279103 A318734 * A127800 A035692 A308654

Adjacent sequences: A029314 A029315 A029316 * A029318 A029319 A029320

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved