A326338 Number of simple graphs with vertices {1..n} whose weakly nesting edges are connected.

1, 1, 2, 7, 48, 781, 27518

Offset

0,3

Comments

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

Links

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

Gus Wiseman, The a(4) = 48 weakly nesting-connected graphs.

Mathematica

wknXQ[eds_]:=MatchQ[eds, {___, {x_, y_}, ___, {z_, t_}, ___}/; (x<=z&&y>=t)||(x>=z&&y<=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]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[csm[Union[List/@#, Select[Subsets[#, {2}], wknXQ]]]]<=1&]], {n, 0, 5}]

Crossrefs

The inverse binomial transform is the covering case A326337.

The non-weak case is A326330.

Cf. A006125, A099947, A136653, A324328, A326289, A326293, A326331, A326335, A326336, A326341.

Sequence in context: A304968 A281263 A206153 * A119668 A101538 A045598

Adjacent sequences: A326335 A326336 A326337 * A326339 A326340 A326341

Keyword

nonn,more

Author

Gus Wiseman, Jun 29 2019

Status

approved