A029295 Expansion of 1/((1-x^3)*(1-x^6)*(1-x^7)*(1-x^11)).

1, 0, 0, 1, 0, 0, 2, 1, 0, 2, 1, 1, 3, 2, 2, 3, 2, 3, 5, 3, 4, 6, 4, 5, 8, 6, 6, 9, 8, 8, 11, 10, 10, 13, 12, 13, 16, 14, 15, 19, 17, 18, 23, 20, 21, 26, 24, 25, 30, 28, 29, 34, 32, 34, 39, 37, 39, 44, 42, 44, 50, 48, 50, 56, 54, 56, 63, 61, 63, 70, 68, 70, 78

Offset

0,7

Comments

Number of partitions of n into parts 3, 6, 7, and 11. - Hoang Xuan Thanh, Apr 07 2026

Links

Table of n, a(n) for n=0..72.

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

Formula

a(n) = floor((2*n^3+81*n^2+678*n+3600)/16632 + ((2*n^2+1) mod 3)*(n+12)/18 + ((4*n^3+n^2+5*n+4) mod 7)/7). - Hoang Xuan Thanh, Apr 07 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^7)(1-x^11)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^6)*(1-x^7)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 07 2026

Crossrefs

Sequence in context: A185207 A185206 A185205 * A185204 A217522 A287520

Adjacent sequences: A029292 A029293 A029294 * A029296 A029297 A029298

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved