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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326279 Number of labeled n-vertex simple graphs containing either a crossing or a nesting pair of edges. 6
0, 0, 0, 0, 28, 864, 32064, 2094064 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

Table of n, a(n) for n=0..7.

FORMULA

A006125(n) = a(n) + A326244(n).

EXAMPLE

The a(4) = 28 edge-sets:

  {13,24}  {12,13,24}  {12,13,14,23}  {12,13,14,23,24}  {12,13,14,23,24,34}

  {14,23}  {12,14,23}  {12,13,14,24}  {12,13,14,23,34}

           {13,14,23}  {12,13,23,24}  {12,13,14,24,34}

           {13,14,24}  {12,13,24,34}  {12,13,23,24,34}

           {13,23,24}  {12,14,23,24}  {12,14,23,24,34}

           {13,24,34}  {12,14,23,34}  {13,14,23,24,34}

           {14,23,24}  {13,14,23,24}

           {14,23,34}  {13,14,23,34}

                       {13,14,24,34}

                       {13,23,24,34}

                       {14,23,24,34}

MATHEMATICA

croXQ[stn_]:=MatchQ[stn, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<y<t||z<x<t<y];

nesXQ[stn_]:=MatchQ[stn, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<t<y||z<x<y<t];

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], croXQ[#]||nesXQ[#]&]], {n, 0, 5}]

CROSSREFS

Crossing and nesting simple graphs are (both) A326210, while non-crossing, non-nesting simple graphs are A326244.

Cf. A000108, A001519, A006125, A016098, A054726, A095661, A324170.

Cf. A326209, A326211, A326248, A326250, A326256.

Sequence in context: A214133 A119055 A324450 * A278195 A095656 A057412

Adjacent sequences:  A326276 A326277 A326278 * A326280 A326281 A326282

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 23 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 August 4 19:54 EDT 2020. Contains 336202 sequences. (Running on oeis4.)