A121272 - OEIS

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

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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: A058410 A005979 A165225 * A346580 A054318 A093140

Adjacent sequences: A121269 A121270 A121271 * A121273 A121274 A121275

KEYWORD

nonn

AUTHOR

Tanya Khovanova, Aug 23 2006

STATUS

approved