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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
OFFSET
1,2
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).
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
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(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