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

1,2

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

Cecilia Bebeacua, Toufik Mansour, Alexander Postnikov, and Simone Severini, On the X-rays of permutations, arXiv:math/0506334 [math.CO], 2005.

Sophie Rehberg, Extensions of Ehrhart theory and applications to combinatorial structures, Ph D. dissertation, Freien Univ. (Berlin, Germany 2025). See pp. 8, 120, 144.

Index entries for sequences related to tournaments

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.

Crossrefs

Cf. A000571, A007747.

Sequence in context: A305547 A007857 A289541 * A020076 A342052 A317873

Adjacent sequences: A047726 A047727 A047728 * A047730 A047731 A047732

Keyword

nonn

Author

David W. Wilson

Status

approved