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 A326247 Number of labeled n-vertex 2-edge multigraphs that are neither crossing nor nesting. 2
 0, 0, 1, 9, 32, 80, 165, 301, 504, 792, 1185, 1705, 2376, 3224, 4277, 5565, 7120, 8976, 11169, 13737, 16720, 20160, 24101, 28589, 33672, 39400, 45825, 53001, 60984, 69832, 79605, 90365, 102176, 115104, 129217, 144585, 161280, 179376, 198949, 220077, 242840 (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 21 2019: (Start) G.f.: x^2*(1 + 4*x - 3*x^2) / (1 - x)^5. a(n) = (n*(12 - 19*n + 6*n^2 + n^3)) / 12. 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 pairs of edges:   {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 October 22 17:34 EDT 2019. Contains 328319 sequences. (Running on oeis4.)