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 A326350 Number of non-nesting connected simple graphs with vertices {1..n}. 2
 1, 0, 1, 4, 23, 157, 1182 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Two edges {a,b}, {c,d} are nesting if a < c < d < b or c < a < b < d. LINKS Gus Wiseman, The a(4) = 23 non-nesting connected simple graphs. Gus Wiseman, The a(5) = 157 non-nesting connected simple graphs. MATHEMATICA 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}]], Union@@#==Range[n]&&Length[csm[#]]<=1&&!MatchQ[#, {___, {x_, y_}, ___, {z_, t_}, ___}/; x

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)