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A326337
Number of simple graphs covering the vertices {1..n} whose weakly nesting edges are connected.
7
1, 0, 1, 3, 29, 595, 23437
OFFSET
0,4
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.
MATHEMATICA
wknXQ[stn_]:=MatchQ[stn, {___, {___, x_, y_, ___}, ___, {___, z_, t_, ___}, ___}/; (x<=z&&y>=t)||(x>=z&&y<=t)];
wknestcmpts[stn_]:=csm[Union[List/@stn, Select[Subsets[stn, {2}], wknXQ]]];
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}]], Union@@#==Range[n]&&Length[wknestcmpts[#]]<=1&]], {n, 0, 5}]
CROSSREFS
The binomial transform is the non-covering case A326338.
The non-weak case is A326331.
Simple graphs whose nesting edges are connected are A326330.
Sequence in context: A210827 A092251 A304553 * A331389 A243435 A064570
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 28 2019
STATUS
approved