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A326351
Number of non-nesting connected simple graphs on a subset of {1..n}.
1
1, 1, 2, 8, 46, 323, 2565
OFFSET
0,3
COMMENTS
Two edges {a,b}, {c,d} are nesting if a < c < d < b or c < a < b < d.
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}]], Length[csm[#]]<=1&&!MatchQ[#, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<t<y||z<x<y<t]&]], {n, 0, 5}]
CROSSREFS
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.
Sequence in context: A334498 A006664 A276367 * A276358 A337060 A141117
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 30 2019
STATUS
approved