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A326329
Number of simple graphs covering {1..n} with no crossing or nesting edges.
9
1, 0, 1, 4, 13, 44, 149, 504, 1705, 5768, 19513, 66012
OFFSET
0,4
COMMENTS
Covering means there are no isolated vertices. Two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b, and nesting if a < c < d < b or c < a < b < d.
Is this (apart from offsets) the same as A073717? - R. J. Mathar, Jul 04 2019
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&!MatchQ[#, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<y<t||z<x<t<y||x<z<t<y||z<x<y<t]&]], {n, 0, 5}]
CROSSREFS
The case for set partitions is A001519.
Covering simple graphs are A006129.
The case with just nesting or just crossing edges forbidden is A324169.
The binomial transform is the non-covering case A326244.
Sequence in context: A273904 A027125 A027127 * A073717 A149427 A290907
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 27 2019
STATUS
approved