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

Author

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

Keywords

• more
• nonn

Comments

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

Links

• 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.

Crossrefs

Cf. A000568, A007079.

Extensions

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