OFFSET
0,4
EXAMPLE
The a(5) = 26 hypergraphs:
{}
{{1,2,3}}
{{1,2,4}}
{{1,2,5}}
{{1,3,4}}
{{1,3,5}}
{{1,4,5}}
{{2,3,4}}
{{2,3,5}}
{{2,4,5}}
{{3,4,5}}
{{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 6 unlabeled 3-uniform hypertrees 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) = 271:
1 X {}
20 X {{1,2,3}}
90 X {{1,2,5},{3,4,5}}
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[stableSets[Subsets[Range[n], {3}], Length[Intersection[#1, #2]]>1&]], {n, 8}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 10 2019
EXTENSIONS
a(9) from Andrew Howroyd, Aug 14 2019
a(10) and a(11) (using A287232) from Joerg Arndt, Oct 12 2023
STATUS
approved