A029313 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^10)*(1-x^11)).

1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 2, 4, 4, 3, 4, 5, 4, 4, 6, 6, 5, 7, 8, 7, 8, 9, 9, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39

Offset

0,11

Comments

Number of partitions of n into parts 3, 7, 10, and 11. - Hoang Xuan Thanh, Apr 10 2026

Links

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

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

Formula

a(n) = floor((2*n^3+93*n^2+1302*n)/27720 - (n mod 3)/9 + ((n^3+n^2+5) mod 7)/7 + ((9*n^3+6*n^2+7*n+4) mod 11)/11). - Hoang Xuan Thanh, Apr 10 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^10)(1-x^11)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 12 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^7)*(1-x^10)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 10 2026

Crossrefs

Sequence in context: A268197 A065382 A066888 * A144001 A124233 A035170

Adjacent sequences: A029310 A029311 A029312 * A029314 A029315 A029316

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved