A064626 Football tournament numbers: the number of possible point series for a tournament of n teams playing each other once where 3 points are awarded to the winning team and 1 to each in the case of a tie.

1, 2, 7, 40, 355, 3678, 37263, 361058, 3403613, 31653377, 292547199, 2696619716

Offset: 1

Author

Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 30 2001

Keywords

• nonn
• nice
• more
• hard

Comments

This sequence reflects the now common 3-point rule of international football where the sum of total points awarded depends on the outcome of each match. The classical 2-point rule is equivalent to that for chess tournaments (A007747).

Examples

			For 2 teams there are 2 possible outcomes: [0, 3] and [1, 1], so a(2) = 2.
For 3 teams the outcomes are [0, 3, 6], [1, 3, 4], [3, 3, 3], [1, 1, 6], [1, 2, 4], [0, 4, 4] and [2, 2, 2], so a(3) is 7. Note that the outcome [3, 3, 3] can be obtained in two ways: (A beats B, B beats C, C beats A) or (B beats A, A beats C, C beats B).
		

Links

• A. Ivanyi, L. Lucz, T. Matuszka, and S. Pirzada, Parallel enumeration of degree sequences of simple graphs, Acta Univ. Sapientiae, Informatica, 4, 2 (2012) 260-288. - From _N. J. A. Sloane_, Feb 15 2013
• Wikipedia, Three points for a win

Crossrefs

Cf. A007747, A047730, A064422, A152789.

Extensions

a(8) and a(9) from Jon E. Schoenfield, May 05 2007

a(10) from Ming Li (dawnli(AT)ustc.edu), Jun 20 2008

a(11) from Jon E. Schoenfield, Sep 04 2008

a(12) from Jon E. Schoenfield, Dec 12 2008