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A121244 Number of score vectors for tournaments on n nodes that do not determine the tournament uniquely. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..27.

Score Sequence at MathWorld

FORMULA

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).

EXAMPLE

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.

CROSSREFS

Sequence in context: A024522 A144841 A203245 * A203574 A070778 A260267

Adjacent sequences:  A121241 A121242 A121243 * A121245 A121246 A121247

KEYWORD

nonn

AUTHOR

Tanya Khovanova, Aug 22 2006

STATUS

approved

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Last modified August 22 10:37 EDT 2017. Contains 290946 sequences.