OFFSET
0,5
COMMENTS
Number of 3-uniform simple hypergraphs on n vertices such that each pair of vertices are together in some edge.
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.
EXAMPLE
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}
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Brendan McKay, Apr 07 2018
STATUS
approved