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A326330 Number of simple graphs with vertices {1..n} whose nesting edges are connected. 8
1, 1, 2, 4, 8, 30, 654 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Two edges {a,b}, {c,d} are nesting if a < c < d < b or c < a < b < d. A graph has its nesting edges connected if the graph whose vertices are the edges and whose edges are nesting pairs of edges is connected.

LINKS

Table of n, a(n) for n=0..6.

Gus Wiseman, The a(5) = 30 nesting-connected simple graphs.

MATHEMATICA

nesXQ[stn_]:=MatchQ[stn, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<t<y||z<x<y<t];

nestcmpts[stn_]:=csm[Union[List/@stn, Select[Subsets[stn, {2}], nesXQ]]];

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[nestcmpts[#]]<=1&]], {n, 0, 5}]

CROSSREFS

The covering case is the inverse binomial transform A326331.

Graphs whose crossing edges are connected are A324328.

Cf. A006125, A007297, A054726, A099947, A117662, A136653, A324328.

Cf. A326210, A326293, A326335, A326336, A326337, A326338, A326339.

Sequence in context: A018346 A006398 A053364 * A018355 A100083 A151406

Adjacent sequences:  A326327 A326328 A326329 * A326331 A326332 A326333

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 27 2019

STATUS

approved

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Last modified January 20 09:40 EST 2021. Contains 340302 sequences. (Running on oeis4.)