A213269 The number of edges in the directed graph of the 2-opt landscape of the symmetric TSP

0, 6, 60, 540, 5040, 50400, 544320, 6350400, 79833600, 1077753600, 15567552000, 239740300800, 3923023104000, 67999067136000, 1244905998336000, 24008901396480000, 486580401635328000, 10339833534750720000, 229909239772692480000, 5339003456943636480000

Offset

3,2

References

J. W. Barnes, B. Dimova, S. P. Dokov, A. Solomon, The theory of elementary landscapes. Applied Mathematics Letters, 16(3):337-343, 2003.

Links

Table of n, a(n) for n=3..22.

Formula

a(n) = n!*(n-3)/4

Example

For a 3 city TSP n=3 there are no edges in the landscape.
For a 4 city TSP there are 6 edges in the directed graph of the 2-opt landscape.

Mathematica

Table[(n!(n-3))/4, {n, 3, 30}] (* Harvey P. Dale, Oct 15 2016 *)

Prog

(GAP)
edges:=n->Factorial(n)*(n-3)/4;
List([3..30], edges);

Crossrefs

Sequence in context: A248217 A102232 A121113 * A091710 A054880 A186656

Adjacent sequences: A213266 A213267 A213268 * A213270 A213271 A213272

Keyword

nonn,easy

Author

Paul John Sutcliffe, Jun 07 2012

Status

approved