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A302394
Number of families of 3-subsets of an n-set that cover all 2-subsets.
17
1, 1, 0, 1, 5, 388, 477965, 19199206747, 48058624241034238, 14791854612528152343049939, 112039538006858119010793653395340973, 42077073837090084518028123082446810913910363417140
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
Sequence in context: A100474 A152438 A060506 * A057633 A193126 A006700
KEYWORD
nonn,hard
AUTHOR
Brendan McKay, Apr 07 2018
STATUS
approved