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 A323293 Number of 3-uniform hypergraphs on n labeled vertices where no two edges have two vertices in common. 6
 1, 1, 1, 2, 5, 26, 271, 5596, 231577, 21286940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS 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 Cf. A000665, A025035, A125791, A190865, A289837, A302374, A302394, A319540, A320395, A322451, A323292-A323299. Sequence in context: A180749 A323299 A111195 * A258868 A322705 A167007 Adjacent sequences:  A323290 A323291 A323292 * A323294 A323295 A323296 KEYWORD nonn,more AUTHOR Gus Wiseman, Jan 10 2019 EXTENSIONS a(9) from Andrew Howroyd, Aug 14 2019 STATUS approved

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Last modified May 26 16:44 EDT 2020. Contains 334626 sequences. (Running on oeis4.)