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

1,5

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).

Links

Table of n, a(n) for n=1..17.

Eric Weisstein's World of Mathematics, Score Sequence.

Formula

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

Example

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.

Crossrefs

Cf. A000568, A000570.

Sequence in context: A377638 A005979 A165225 * A346580 A054318 A093140

Adjacent sequences: A121269 A121270 A121271 * A121273 A121274 A121275

Keyword

nonn

Author

Tanya Khovanova, Aug 23 2006

Status

approved