A326350 -id:A326350 - cp's OEIS frontend

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A326351 Number of non-nesting connected simple graphs on a subset of {1..n}.

Original entry on oeis.org

1, 1, 2, 8, 46, 323, 2565

Offset: 0

Gus Wiseman, Jun 30 2019

Two edges {a,b}, {c,d} are nesting if a < c < d < b or c < a < b < d.

The binomial transform is the covering case A326350.
Connected simple graphs are A001349.
Connected simple graphs with no crossing or nesting edges are A326294.
Simple graphs without crossing or nesting edges are A326244.
Cf. A006125, A054726, A117662, A136653.
Cf. A324169, A326210, A326293, A326329, A326340.

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Length[csm[#]]<=1&&!MatchQ[#,{_,{x_,y_},_,{z_,t_},_}/;x

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