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 A326339 Number of connected simple graphs with vertices {1..n} and no crossing or nesting edges. 6
 1, 0, 1, 4, 12, 36, 108, 324 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. Appears to be essentially the same as A003946. LINKS Table of n, a(n) for n=0..7. Gus Wiseman, The a(5) = 36 connected graphs with no crossing or nesting edges. Gus Wiseman, The a(6) = 108 connected graphs with no crossing or nesting edges. EXAMPLE The a(2) = 1 through a(4) = 36 edge-sets: {12} {12,13} {12,13,14} {12,23} {12,13,34} {13,23} {12,14,34} {12,13,23} {12,23,24} {12,23,34} {12,24,34} {13,23,34} {14,24,34} {12,13,14,34} {12,13,23,34} {12,14,24,34} {12,23,24,34} MATHEMATICA 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[csm[#]]<=1&&!MatchQ[#, {___, {x_, y_}, ___, {z_, t_}, ___}/; x

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)