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 A330057 Number of set-systems covering n vertices with no singletons or endpoints. 3
 1, 0, 0, 5, 1703 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A set-system is a finite set of finite nonempty set of positive integers. A singleton is an edge of size 1. An endpoint is a vertex appearing only once (degree 1). LINKS Wikipedia, Degree (graph theory) FORMULA Binomial transform is A330056. EXAMPLE The a(3) = 5 set-systems: {{1,2},{1,3},{2,3}} {{1,2},{1,3},{1,2,3}} {{1,2},{2,3},{1,2,3}} {{1,3},{2,3},{1,2,3}} {{1,2},{1,3},{2,3},{1,2,3}} MATHEMATICA Table[Length[Select[Subsets[Subsets[Range[n], {2, n}]], Union@@#==Range[n]&&Min@@Length/@Split[Sort[Join@@#]]>1&]], {n, 0, 4}] CROSSREFS The version for non-isomorphic set-systems is A330055 (by weight). The non-covering version is A330056. Set-systems with no singletons are A016031. Set-systems with no endpoints are A330059. Non-isomorphic set-systems with no singletons are A306005 (by weight). Non-isomorphic set-systems with no endpoints are A330054 (by weight). Non-isomorphic set-systems counted by vertices are A000612. Non-isomorphic set-systems counted by weight are A283877. Cf. A007716, A055621, A302545, A317533, A317794, A319559, A320665, A321405, A330052, A330058. Sequence in context: A198246 A122465 A203683 * A324265 A003733 A201300 Adjacent sequences: A330054 A330055 A330056 * A330058 A330059 A330060 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 30 2019 STATUS approved

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Last modified December 1 01:13 EST 2022. Contains 358453 sequences. (Running on oeis4.)