A326350 - OEIS

%I #6 Jun 30 2019 06:51:00

%S 1,0,1,4,23,157,1182

%N Number of non-nesting connected simple graphs with vertices {1..n}.

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

%H Gus Wiseman, <a href="/A326350/a326350.png">The a(4) = 23 non-nesting connected simple graphs</a>.

%H Gus Wiseman, <a href="/A326350/a326350_1.png">The a(5) = 157 non-nesting connected simple graphs</a>.

%t 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]]]]]]]]];

%t Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Union@@#==Range[n]&&Length[csm[#]]<=1&&!MatchQ[#,{___,{x_,y_},___,{z_,t_},___}/;x<z<t<y||z<x<y<t]&]],{n,0,5}]

%Y The inverse binomial transform is the non-covering case A326351.

%Y Connected simple graphs are A001349.

%Y Connected simple graphs with no crossing or nesting edges are A326294.

%Y Simple graphs without crossing or nesting edges are A326244.

%Y Cf. A006125, A054726, A117662, A136653.

%Y Cf. A324169, A326210, A326293, A326329, A326340.

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Jun 30 2019