A135388 Number of (directed) Eulerian circuits on the complete graph K_{2n+1}.

2, 264, 129976320, 911520057021235200, 257326999238092967427785160130560, 6705710151431658873046319662156165939200000000000000, 32132958735643556926111996291480203406145819659840760945049600000000000000000

Offset

1,1

References

B. D. McKay, Applications of a technique for labeled enumeration, Congress. Numerantium, 40 (1983), 207-221.

Links

Table of n, a(n) for n=1..7.

Brendan D. McKay and Robert W. Robinson, Asymptotic enumeration of Eulerian circuits in the complete graph, Combinatorics, Probability and Computing, 7 (1998), 437-449.

G. Tarry, Géométrie de situation: Nombre de manières distinctes de parcourir en une seule course toutes les allées d'un labyrinthe rentrant, en ne passant qu'une seule fois par chacune des allées, Comptes Rendus Assoc. Franç. Avance. Sci. 15, part 2 (1886), pp. 49-53.

Eric Weisstein's World of Mathematics, Complete Graph

Eric Weisstein's World of Mathematics, Eulerian Cycle

Formula

a(n) = A007082(n) * (n-1)!^(2*n+1).

a(n) = A350028(2n+1) = A357887(2n+1,n(2n+1)). - Max Alekseyev, Oct 19 2022

Mathematica

Table[2 Length[FindEulerianCycle[CompleteGraph[2 n + 1], All]], {n, 3}] (* Eric W. Weisstein, Jan 09 2018 *)
  (* a(3) requires a very large amount of memory *)

Crossrefs

Bisection of A350028.

Cf. A007082, A232545, A357856, A357857, A356366, A357855, A357885, A357886, A357887.

Sequence in context: A137105 A216984 A007082 * A238983 A188964 A278771

Adjacent sequences: A135385 A135386 A135387 * A135389 A135390 A135391

Keyword

nonn,walk

Author

Max Alekseyev, Dec 10 2007

Status

approved