

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


LINKS



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



KEYWORD

nonn,nice,more,hard


AUTHOR

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


EXTENSIONS

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


STATUS

approved



