login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326251 Number of digraphs with vertices {1..n} whose increasing edges are not crossing. 5
1, 2, 16, 512, 49152, 11534336, 6039797760, 6768868458496, 15885743998107648, 77083611222073409536, 767126299049285413502976, 15572324598183490228037091328, 642316330843573124053884695740416, 53681919993405760099480940765478125568 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

Conjecture: Also the number of non-nesting digraphs with vertices {1..n} whose increasing edges are not crossing, where two edges (a,b), (c,d) are nesting if a < c < d < b or c < a < b < d.

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = 2^(n * (n + 1)/2) * A054726(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 non-crossing are A054726.

Digraphs whose edges are not crossing are A326237.

Digraphs whose increasing edges are crossing are A326252.

Cf. A002416, A229865, A324170, A326209, A326250, A326251.

Sequence in context: A265015 A267728 A063387 * A228979 A293150 A286039

Adjacent sequences:  A326248 A326249 A326250 * A326252 A326253 A326254

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 30 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 21:20 EST 2021. Contains 349426 sequences. (Running on oeis4.)