%I #12 Nov 01 2019 18:38:35

%S 0,0,0,0,5,45,438,6849,191483,9732967,903753099,154108310917,

%T 48542114686488,28401423719121589,31021002160355165644,

%U 63530415842308265098260,244912778438520759443242406

%N Number of outcomes of unlabeled n-team round-robin tournaments that are not uniquely defined by their score vectors.

%C This sequence is the difference between A000568 (Number of outcomes of unlabeled n-team round-robin tournaments) and A000570 (Number of tournaments on n nodes determined by their score vectors).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ScoreSequence.html">Score Sequence</a>.

%F a(n) = A000568(n) - A000570(n). - _Michel Marcus_, Nov 01 2019

%e All tournaments with 4 or fewer teams are uniquely defined by their score vectors. Hence a(1) = a(2) = a(3) = a(4) = 0.

%e For five-team tournaments only two score sequences do not define the tournament uniquely: {1,1,2,3,3} and {1,2,2,2,3}. The first sequence corresponds to two different tournaments and the second sequence to three different tournaments. Thus a(5) = 5.

%Y Cf. A000568, A000570.

%K nonn

%O 1,5

%A _Tanya Khovanova_, Aug 23 2006