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A121244
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Number of score vectors for tournaments on n nodes that do not determine the tournament uniquely.
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0
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0, 0, 0, 0, 2, 11, 41, 136, 437, 1397, 4490, 14554, 47683, 158093, 530265, 1797631, 6153650, 21252343, 73986392, 259434758, 915667537, 3251026851, 11605063370, 41631062856, 150021553132, 542875085143, 1972049524959
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OFFSET
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1,5
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LINKS
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FORMULA
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This sequence is the difference between A000571 (Number of different scores that are possible in an n-team round-robin tournament) and A000570 (Number of tournaments on n nodes determined by their score vectors).
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EXAMPLE
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For n = 3 there are two possible score sequences: {0,1,2} and {1,1,1}. Both of them uniquely define the corresponding tournament. Hence a(3) = 0.
The first occurrence of a sequence that doesn't define a tournament happens for n = 5. There are two such sequences {1,1,2,3,3} and {1,2,2,2,3}. Let's consider the first sequence: {1,1,2,3,3}. Let's take the two best players - the persons with 3 wins - as one of them should win the game with another, there is only one other person who won a game with one of the two best players. It could happen that this player has score 1 or 2. Thus we can get two different tournaments with the same score vector.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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