A055538 - OEIS

A055538

Number of asymmetric types of (3,n)-hypergraphs without isolated nodes, under action of symmetric group S_3; asymmetric n-covers of an unlabeled 3-set.

4, 20, 65, 170, 383, 779, 1470, 2611, 4418, 7182, 11283, 17213, 25601, 37230, 53074, 74327, 102434, 139133, 186501, 246988, 323479, 419344, 538492, 685438, 865376, 1084236, 1348777, 1666664, 2046551, 2498179, 3032482, 3661673, 4399374

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OFFSET

3,1

COMMENTS

Cover may include both empty sets and multiple occurrences of a subset.

LINKS

Table of n, a(n) for n=3..35.

FORMULA

G.f. : (1/(1-x)^8-3/(1-x)^4/(1-x^2)^2+2/(1-x)^2/(1-x^3)^2-3/(1-x)^4+3/(1-x)^2/(1-x^2)+6/(1-x)^2-6/(1-x))/6.

EXAMPLE

There are 4 asymmetric (3,3)-hypergraphs without isolated nodes: {{1,2},{1,2},{1,3}}, {{1},{1,2},{1,2,3}}, {{1},{1,2},{2,3}}, {{1},{2},{1,3}}.

CROSSREFS