A302394 Number of families of 3-subsets of an n-set that cover all 2-subsets.

1, 1, 0, 1, 5, 388, 477965, 19199206747, 48058624241034238, 14791854612528152343049939, 112039538006858119010793653395340973, 42077073837090084518028123082446810913910363417140

Offset: 0

Author

Brendan McKay, Apr 07 2018

Keywords

• nonn
• hard

Comments

Number of 3-uniform simple hypergraphs on n vertices such that each pair of vertices are together in some edge.

Examples

			For n=4 the a(4)=5 solutions are {123,124,134}, {123,124,234},{123,134,234},{124,134,234}, {123,124,134,234}
		

Formula

a(n) = SUM (-1)^e(G) (n!/a(G)) 2^t(G), where the sum is over the unlabeled graphs G with n vertices, e(G) is the number of edges in the complement of G, a(G) is the order of the automorphism group of G, and t(G) is the number of triangles in G.