A121272 Number of outcomes of unlabeled n-team round-robin tournaments that are not uniquely defined by their score vectors.

0, 0, 0, 0, 5, 45, 438, 6849, 191483, 9732967, 903753099, 154108310917, 48542114686488, 28401423719121589, 31021002160355165644, 63530415842308265098260, 244912778438520759443242406

Offset: 1

Author

Tanya Khovanova, Aug 23 2006

Keywords

• nonn

Comments

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).

Examples

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

Links

• Eric Weisstein's World of Mathematics, Score Sequence.

Crossrefs

Cf. A000568, A000570.

Formula

a(n) = A000568(n) - A000570(n). - Michel Marcus, Nov 01 2019