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 A326330 Number of simple graphs with vertices {1..n} whose nesting edges are connected. 8
 1, 1, 2, 4, 8, 30, 654 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 Gus Wiseman, The a(5) = 30 nesting-connected simple graphs. MATHEMATICA nesXQ[stn_]:=MatchQ[stn, {___, {x_, y_}, ___, {z_, t_}, ___}/; x0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[]], Union@@s[[c[]]]]]]]]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[nestcmpts[#]]<=1&]], {n, 0, 5}] CROSSREFS The covering case is the inverse binomial transform A326331. Graphs whose crossing edges are connected are A324328. Cf. A006125, A007297, A054726, A099947, A117662, A136653, A324328. Cf. A326210, A326293, A326335, A326336, A326337, A326338, A326339. Sequence in context: A018346 A006398 A053364 * A018355 A100083 A151406 Adjacent sequences:  A326327 A326328 A326329 * A326331 A326332 A326333 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 27 2019 STATUS approved

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Last modified January 20 09:40 EST 2021. Contains 340302 sequences. (Running on oeis4.)