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A326338 Number of simple graphs with vertices {1..n} whose weakly nesting edges are connected. 5
1, 1, 2, 7, 48, 781, 27518 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A304968 A281263 A206153 * A119668 A101538 A045598
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 29 2019
STATUS
approved

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Last modified June 13 10:09 EDT 2024. Contains 373383 sequences. (Running on oeis4.)