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 A326244 Number of labeled n-vertex simple graphs without crossing or nesting edges. 18
 1, 1, 2, 8, 36, 160, 704, 3088, 13536, 59328, 260032, 1139712 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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. LINKS Table of n, a(n) for n=0..11. Eric Marberg, Crossings and nestings in colored set partitions, arXiv preprint arXiv:1203.5738 [math.CO], 2012. Gus Wiseman, The a(4) = 36 non-crossing, non-nesting simple labeled graphs. FORMULA A006125(n) = a(n) + A326279(n). Conjectures from Colin Barker, Jun 28 2019: (Start) G.f.: (1 - x)*(1 - 4*x) / (1 - 6*x + 8*x^2 - 4*x^3). a(n) = 6*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>2. (End) MATHEMATICA croXQ[stn_]:=MatchQ[stn, {___, {x_, y_}, ___, {z_, t_}, ___}/; x

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Last modified October 4 17:22 EDT 2023. Contains 365887 sequences. (Running on oeis4.)