A047730 Number of score sequences in tournament with n players, when 4 points are awarded in each game.

1, 3, 13, 76, 521, 3996, 32923, 286202, 2590347, 24203935, 232050202, 2272449745, 22653570386, 229274897514, 2350933487206, 24381053759852, 255382755251622, 2698732882975782, 28743579211912338

Offset: 1

Author

David W. Wilson

Keywords

• nonn

References

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

Links

• Qihao Ye, Table of n, a(n) for n = 1..928
• Index entries for sequences related to tournaments

Crossrefs

Cf. A000571, A007747, A047729, A064626, A064422.

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}) <= 4, p_i >= 0, i=1, ..., n.