A029299 Expansion of 1/((1-x^3)*(1-x^6)*(1-x^8)*(1-x^11)).

1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 3, 0, 3, 3, 1, 4, 4, 2, 5, 4, 4, 6, 6, 5, 7, 7, 7, 8, 10, 8, 10, 12, 10, 12, 15, 11, 15, 17, 14, 18, 20, 16, 22, 22, 20, 25, 26, 23, 29, 29, 28, 32, 34, 32, 37, 38, 37, 41, 44, 41, 47, 49, 47

Offset

0,7

Comments

Number of partitions of n into parts 3, 6, 8, and 11. - Hoang Xuan Thanh, Apr 08 2026

Links

Table of n, a(n) for n=0..64.

Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,1,0,1,-1,0,0,0,0,-2,0,0,0,0,-1,1,0,1,0,0,1,0,0,-1).

Formula

a(n) = floor((n^3+42*n^2+756*n+5616)/9504 - (n mod 2)*n/96 - ((2*n^2+2*n) mod 3)*(n+18)/18 - ((2*n^2+n) mod 3)/3 + ((9*n^3+4*n^2+6*n+10) mod 11)/11 + [(n mod 11)=6] - [(n mod 11)=10]). - Hoang Xuan Thanh, Apr 08 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^8)(1-x^11)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)
LinearRecurrence[{0, 0, 1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 3, 0, 3, 3, 1, 4, 4, 2, 5, 4, 4, 6, 6, 5, 7, 7}, 70] (* Harvey P. Dale, Mar 04 2021 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^6)*(1-x^8)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 08 2026

Crossrefs

Sequence in context: A004548 A125921 A321457 * A309953 A281666 A049803

Adjacent sequences: A029296 A029297 A029298 * A029300 A029301 A029302

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved