A323292 Number of 3-uniform hypergraphs spanning n labeled vertices where no two edges have two vertices in common.

1, 0, 0, 1, 0, 15, 160, 4125, 193200, 19384225

Offset

0,6

Links

Table of n, a(n) for n=0..9.

Formula

Inverse binomial transform of A323293. - Andrew Howroyd, Aug 14 2019

Example

The a(5) = 15 hypergraphs:
  {{1,2,3},{1,4,5}}
  {{1,2,3},{2,4,5}}
  {{1,2,3},{3,4,5}}
  {{1,2,4},{1,3,5}}
  {{1,2,4},{2,3,5}}
  {{1,2,4},{3,4,5}}
  {{1,2,5},{1,3,4}}
  {{1,2,5},{2,3,4}}
  {{1,2,5},{3,4,5}}
  {{1,3,4},{2,3,5}}
  {{1,3,4},{2,4,5}}
  {{1,3,5},{2,3,4}}
  {{1,3,5},{2,4,5}}
  {{1,4,5},{2,3,4}}
  {{1,4,5},{2,3,5}}
Non-isomorphic representatives of the 3 unlabeled 3-uniform hypergraphs spanning 6 vertices where no two edges have two vertices in common, and their multiplicities in the labeled case which add up to a(6) = 160:
   10 X {{1,2,3},{4,5,6}}
  120 X {{1,3,5},{2,3,6},{4,5,6}}
   30 X {{1,2,4},{1,3,5},{2,3,6},{4,5,6}}

Mathematica

stableSets[u_, Q_]:=If[Length[u]===0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r===w||Q[r, w]||Q[w, r]], Q]]]];
Table[Length[Select[stableSets[Subsets[Range[n], {3}], Length[Intersection[#1, #2]]>=2&], Union@@#==Range[n]&]], {n, 6}]

Crossrefs

Cf. A000665, A025035, A125791, A190865, A289837, A302374, A302394, A320395, A322451, A323293-A323299.

Sequence in context: A021048 A095685 A263514 * A067361 A014920 A081034

Adjacent sequences: A323289 A323290 A323291 * A323293 A323294 A323295

Keyword

nonn,more

Author

Gus Wiseman, Jan 10 2019

Extensions

a(9) from Andrew Howroyd, Aug 14 2019

Status

approved