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A326331 Number of simple graphs covering the vertices {1..n} whose nesting edges are connected. 6
1, 0, 1, 0, 1, 14, 539 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
Covering means there are no isolated vertices. 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
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}]], Union@@#==Range[n]&&Length[nestcmpts[#]]<=1&]], {n, 0, 5}]
CROSSREFS
The non-covering case is the binomial transform A326330.
Covering graphs whose crossing edges are connected are A324327.
Sequence in context: A209096 A159645 A297805 * A210029 A292966 A109773
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 27 2019
STATUS
approved

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Last modified July 24 01:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)