A007079 -id:A007079 - cp's OEIS frontend

A096368 Number of unlabeled regular tournaments with 2n+1 nodes.

1, 1, 1, 3, 15, 1223, 1495297, 18400989629, 2406183070160597, 3511056114693589781331, 59423289286172717542785192911, 12034362241475984037791303316068785847, 29921426689289629541982244885554389482859734381

Offset: 0

David J. Haglin (david.haglin(AT)mnsu.edu), Jul 02 2004

Terms may be computed without generating each tournament by enumerating the number of tournaments by degree sequence. A PARI program showing this technique for labeled tournaments is given in A007079. Burnside's lemma as applied in A000568 can be used to extend this method to the unlabeled case. - Andrew Howroyd, Mar 13 2020

Gunnar Brinkmann, Generating regular directed graphs, Discrete Math., 313 (2012), 1-7. [_N. J. A. Sloane_, Nov 26 2012]
Marc Chamberland and Eugene A. Herman, Rock-paper-scissors meets Borromean rings, The Mathematical Intelligencer, 37(2), 20--25.
Marc Chamberland, What's Better than Rock Paper Scissors? (2014).
B. D. McKay, Catalogues of directed graphs.
B. D. McKay, The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs, Combinatorica 10 (1990), 367-377.

Cf. A000568, A007079.

Offset and count for 15 vertices corrected by Brendan McKay, Dec 09 2008
a(0) from Álvar Ibeas, Nov 18 2017
a(8)-a(12) from Andrew Howroyd, Mar 13 2020

A334554 Number of Eulerian orientations in the n-cocktail party graph.

Original entry on oeis.org

1, 2, 38, 6936, 14747896, 394274110160, 138804098924751280

Offset: 1

Andrew Howroyd, May 22 2020

An Eulerian orientation of a graph is an orientation of the edges such that every vertex has in-degree equal to out-degree.

The corresponding sequence for the complete graph on 2n+1 vertices is A007079.

Eric Weisstein's World of Mathematics, Cocktail Party Graph

Cf. A007079, A297383.

cp's OEIS Frontend

A096368 Number of unlabeled regular tournaments with 2n+1 nodes.

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