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%I #31 Jul 24 2021 23:23:27
%S 1,2,7,40,355,3678,37263,361058,3403613,31653377,292547199,2696619716
%N 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.
%C 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).
%H A. Ivanyi, L. Lucz, T. Matuszka, and S. Pirzada, <a href="http://www.acta.sapientia.ro/acta-info/C4-2/info42-7.pdf">Parallel enumeration of degree sequences of simple graphs</a>, Acta Univ. Sapientiae, Informatica, 4, 2 (2012) 260-288. - From _N. J. A. Sloane_, Feb 15 2013
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Three_points_for_a_win">Three points for a win</a>
%e For 2 teams there are 2 possible outcomes: [0, 3] and [1, 1], so a(2) = 2.
%e 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).
%Y Cf. A007747, A047730, A064422, A152789.
%K nonn,nice,more,hard
%O 1,2
%A Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 30 2001
%E a(8) and a(9) from _Jon E. Schoenfield_, May 05 2007
%E a(10) from Ming Li (dawnli(AT)ustc.edu), Jun 20 2008
%E a(11) from _Jon E. Schoenfield_, Sep 04 2008
%E a(12) from _Jon E. Schoenfield_, Dec 12 2008
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