A326252 Number of digraphs with vertices {1..n} whose increasing edges are crossing.

0, 0, 0, 0, 16384, 22020096, 62679678976, 556181084962816, 18430858329711443968, 2417774555618036276002816, 1267649833101930352211289702400, 2658455975997507147624123892523597824, 22300745197888306810692145148594476810240000

Offset

0,5

Comments

A directed edge (a,b) is increasing if a < b. Two edges (a,b), (c,d) are crossing if a < c < b < d or c < a < d < b.

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = 2^(n * (n + 1)/2) * A326210(n).

Mathematica

croXQ[eds_]:=MatchQ[eds, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<y<t||z<x<t<y];
Table[Length[Select[Subsets[Tuples[Range[n], 2]], croXQ[#]&]], {n, 0, 4}]

Crossrefs

Simple graphs whose edges are crossing are A326210.

Digraphs whose increasing edges are not crossing are A326251.

Digraphs whose edges are not crossing are A326237.

Cf. A002416, A002720, A229865, A324170, A326209, A326252, A326258.

Sequence in context: A224286 A224209 A017035 * A269295 A017119 A017215

Adjacent sequences: A326249 A326250 A326251 * A326253 A326254 A326255

Keyword

nonn

Author

Gus Wiseman, Jun 30 2019

Extensions

a(8)-a(12) added from formula by Falk Hüffner, Jun 07 2026

Status

approved