A321134 Number of uniform hypergraphs spanning n vertices where every two vertices appear together in some edge.

1, 1, 1, 2, 7, 406, 505635

Offset

0,4

Comments

A hypergraph is uniform if all edges have the same size.

Links

Table of n, a(n) for n=0..6.

Example

The a(4) = 7 hypergraphs:
  {{1,2,3,4}}
  {{1,2,3},{1,2,4},{1,3,4}}
  {{1,2,3},{1,2,4},{2,3,4}}
  {{1,2,3},{1,3,4},{2,3,4}}
  {{1,2,4},{1,3,4},{2,3,4}}
  {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
  {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

Mathematica

Table[Sum[Length[Select[Subsets[Subsets[Range[n], {k}]], And[Union@@#==Range[n], Length[Union@@(Subsets[#, {2}]&/@#)]==Binomial[n, 2]]&]], {k, 1, n}], {n, 1, 6}]

Crossrefs

Row sums of A320606.

Cf. A058891, A299353, A302394, A306021, A319189, A320444.

Sequence in context: A262088 A110386 A260229 * A027732 A073698 A073860

Adjacent sequences: A321131 A321132 A321133 * A321135 A321136 A321137

Keyword

nonn,more

Author

Gus Wiseman, Jan 10 2019

Status

approved