A379758 Number of sequences in which the games of a fully symmetric single-elimination tournament with 2^n teams can be played if arbitrarily many arenas are available.

1, 3, 365, 1323338487, 1119556146543237253601352961, 3414445659328795239581367793706562556567987857578516541118092297328702035

Offset

1,2

Comments

a(n) is also the number of tie-permitting labeled histories for a fully symmetric labeled topology with 2^n leaves.

Links

Table of n, a(n) for n=1..6.

M. C. King and N. A. Rosenberg, A mathematical connection between single-elimination sports tournaments and evolutionary trees, Math. Mag. 96 (2023), 484-497.

Formula

a(n) = Sum_{k=n..2^n-1} A380166(n,k).

Example

For n=2 and a tournament with structure ((A,B),(C,D)), game (A,B) can be played before, after, or simultaneously with game (C,D), producing a(2)=3.

Crossrefs

Cf. A056972 (game sequences with only one arena).

a(n) gives row sums for A380166(n,k).

Sequence in context: A324427 A304285 A324269 * A173648 A110717 A068988

Adjacent sequences: A379753 A379754 A379755 * A379759 A379760 A379761

Keyword

nonn,new

Author

Noah A Rosenberg, Jan 01 2025

Status

approved