A047729 Number of score sequences in tournament with n players, when 3 points are awarded in each game.

1, 2, 8, 37, 198, 1178, 7548, 50944, 357855, 2595250, 19313372, 146815503, 1136158495, 8927025989, 71065654235, 572215412354, 4653746621835, 38184724333615, 315792633485360, 2630183440412617, 22046522161472304

Offset: 1

Author

David W. Wilson

Keywords

• nonn

References

• P. A. MacMahon, Chess tournaments and the like treated by the calculus of symmetric functions, Coll. Papers I, MIT Press, 344-375.

Links

• Qihao Ye, Table of n, a(n) for n = 1..1032
• C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, On the X-rays of permutations, arXiv:math/0506334 [math.CO], 2005.
• Index entries for sequences related to tournaments

Crossrefs

Cf. A000571, A007747.

Formula

Nonnegative integer points (p_1, p_2, ..., p_n) in polytope p_0=p_{n+1}=0, 2p_i -(p_{i+1}+p_{i-1}) <= 3, p_i >= 0, i=1, ..., n.