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 A324169 Number of labeled graphs covering the vertex set {1,...,n} with no crossing edges. 26
 1, 0, 1, 4, 25, 176, 1353, 11012, 93329, 815104, 7285489, 66324644, 612863337, 5733381616, 54195878137, 516852285668, 4966883732129, 48049936644736, 467566946973537, 4573486005681092, 44942852084894777, 443484037981300144, 4392621673072766505 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Two edges {x,y}, {z,t} are crossing if either x < z < y < t or z < x < t < y. If the vertices are arranged in a circle, this is equivalent to crossing of chords. Covering means there are no isolated vertices. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 Gus Wiseman, The a(4) = 25 graphs covering {1,2,3,4} with no crossing edges. Gus Wiseman, The a(5) = 176 graphs covering 5 vertices with no crossing edges, radial embedding. FORMULA Inverse binomial transform of A054726. G.f.: (2 + 7*x + 3*x^2 - x*sqrt(1 - 10*x - 7*x^2))/(2*(1 + x)^3). - Andrew Howroyd, Jan 20 2023 MATHEMATICA nn=8; croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x

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Last modified August 11 22:07 EDT 2024. Contains 375076 sequences. (Running on oeis4.)