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 A324327 Number of topologically connected chord graphs covering {1,...,n}. 14
 1, 0, 1, 0, 1, 11, 257 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A graph is topologically connected if the graph whose vertices are the edges and whose edges are crossing pairs of edges is connected, where two edges cross each other if they are of the form {{x,y},{z,t}} with x < z < y < t or z < x < t < y. Covering means there are no isolated vertices. LINKS Gus Wiseman, The a(5) = 11 topologically connected chord graphs. Gus Wiseman, The a(6) = 257 topologically connected chord graphs. FORMULA Inverse binomial transform of A324328. EXAMPLE The a(0) = 1 through a(5) = 11 graphs:   {}  {{12}}  {{13}{24}}  {{13}{14}{25}}                           {{13}{24}{25}}                           {{13}{24}{35}}                           {{14}{24}{35}}                           {{14}{25}{35}}                           {{13}{14}{24}{25}}                           {{13}{14}{24}{35}}                           {{13}{14}{25}{35}}                           {{13}{24}{25}{35}}                           {{14}{24}{25}{35}}                           {{13}{14}{24}{25}{35}} MATHEMATICA croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; crosscmpts[stn_]:=csm[Union[Subsets[stn, {1}], Select[Subsets[stn, {2}], croXQ]]]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], And[Union@@#==Range[n], Length[crosscmpts[#]]<=1]&]], {n, 0, 5}] CROSSREFS Cf. A000108, A000699 (the case with disjoint edges), A001764, A002061, A007297, A016098, A054726, A099947, A136653 (the case with set-theoretical connectedness also), A268814. Cf. A324167, A324169 (non-crossing covers), A324172, A324173, A324323, A324328 (non-covering case). Sequence in context: A052782 A186249 A186250 * A142208 A168466 A091159 Adjacent sequences:  A324324 A324325 A324326 * A324328 A324329 A324330 KEYWORD nonn,more AUTHOR Gus Wiseman, Feb 22 2019 STATUS approved

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Last modified April 10 16:05 EDT 2021. Contains 342845 sequences. (Running on oeis4.)