A323292 - OEIS

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

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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