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Search: id:A064626
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| A064626 |
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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. |
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+0
5
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| 1, 2, 7, 40, 355, 3678, 37263, 361058, 3403613, 31653377, 292547199, 2696619716
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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).
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EXAMPLE
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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.
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CROSSREFS
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Cf. A007747, A047730, A064422, A152789.
Sequence in context: A102317 A031973 A132785 this_sequence A137731 A008608 A028441
Adjacent sequences: A064623 A064624 A064625 this_sequence A064627 A064628 A064629
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KEYWORD
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nonn,nice,more,hard
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AUTHOR
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Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 30 2001
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EXTENSIONS
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a(8) and a(9) from Jon Schoenfield (jonscho(AT)hiwaay.net), May 05 2007
a(10) from Ming Li (dawnli(AT)ustc.edu), Jun 20 2008
a(11) from Jon Schoenfield (jonscho(AT)hiwaay.net), Sep 04 2008
a(12) from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Dec 12 2008
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