OFFSET

1,5

LINKS

Eric Weisstein's World of Mathematics, Score Sequence.

FORMULA

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

KEYWORD

nonn

AUTHOR

Tanya Khovanova, Aug 22 2006

STATUS

approved