

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.


7



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

1,2


COMMENTS

This series 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).


LINKS

Table of n, a(n) for n=1..12.
A. Ivanyi, L. Lucz, T. Matuszka, and S. Pirzada, Parallel enumeration of degree sequences of simple graphs, Acta Univ. Sapientiae, Informatica, 4, 2 (2012) 260288.  From N. J. A. Sloane, Feb 15 2013
Wikipedia, Three points for a win


EXAMPLE

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).


CROSSREFS

Cf. A007747, A047730, A064422, A152789.
Sequence in context: A319945 A132785 A224677 * A137731 A008608 A028441
Adjacent sequences: A064623 A064624 A064625 * A064627 A064628 A064629


KEYWORD

nonn,nice,more,hard


AUTHOR

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


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


STATUS

approved



