|
|
A121272
|
|
Number of outcomes of unlabeled n-team round-robin tournaments that are not uniquely defined by their score vectors.
|
|
0
|
|
|
0, 0, 0, 0, 5, 45, 438, 6849, 191483, 9732967, 903753099, 154108310917, 48542114686488, 28401423719121589, 31021002160355165644, 63530415842308265098260, 244912778438520759443242406
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|