A029159 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^7)*(1-x^11)).

1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 11, 12, 13, 14, 16, 17, 18, 20, 22, 23, 25, 27, 29, 31, 33, 36, 38, 40, 43, 46, 48, 51, 55, 57, 61, 64, 68, 71, 75, 79, 83, 87, 91, 96, 100, 105, 110, 115, 120, 125

Offset

0,7

Comments

a(n) is the number of partitions of n into parts 2, 3, 7, and 11. - Hoang Xuan Thanh, Oct 05 2025

Links

Table of n, a(n) for n=0..59.

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

Formula

a(n) = floor((46*n^3+327*n^2+522*n)/504) - floor((n^3+7*n^2+10*n-6)/11). - Hoang Xuan Thanh, Oct 05 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^7)(1-x^11)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, -1, 0, 1, 0, -1, -1, 1, 1, -1, -1, 0, 1, 0, -1, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 11, 12, 13}, 60] (* Harvey P. Dale, Apr 01 2016 *) (* Harvey P. Dale, Apr 01 2016 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^7)*(1-x^11)) + O(x^60)) \\ Hoang Xuan Thanh, Oct 05 2025

Crossrefs

Sequence in context: A194161 A394219 A051066 * A029099 A029245 A174576

Adjacent sequences: A029156 A029157 A029158 * A029160 A029161 A029162

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved