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 A326278 Number of n-vertex, 2-edge multigraphs that are not nesting. Number of n-vertex, 2-edge multigraphs that are not crossing. 0
 0, 0, 1, 9, 34, 90, 195, 371, 644, 1044, 1605, 2365, 3366, 4654, 6279, 8295, 10760, 13736, 17289, 21489, 26410, 32130, 38731, 46299, 54924, 64700, 75725, 88101, 101934, 117334, 134415, 153295, 174096, 196944, 221969, 249305, 279090, 311466, 346579, 384579 (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. LINKS FORMULA Conjectures from Colin Barker, Jun 25 2019: (Start) G.f.: x^2*(1 + 4*x - x^2) / (1 - x)^5. a(n) = (n*(3 - 4*n + n^3)) / 6 . a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. (End) EXAMPLE The a(3) = 9 non-crossing multigraphs:   {12,12}   {12,13}   {12,23}   {13,12}   {13,13}   {13,23}   {23,12}   {23,13}   {23,23} MATHEMATICA croXQ[stn_]:=MatchQ[stn, {___, {x_, y_}, ___, {z_, t_}, ___}/; x

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Last modified September 21 12:13 EDT 2020. Contains 337271 sequences. (Running on oeis4.)