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

Author

Noah A Rosenberg, Jan 01 2025

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Emily H. Dickey and Noah A. Rosenberg, Labelled histories with multifurcation and simultaneity, Phil. Trans. R. Soc. B 380 (2025), 20230307. See Table 5.
• Matthew C. King and Noah A. Rosenberg, A mathematical connection between single-elimination sports tournaments and evolutionary trees, Math. Mag. 96 (2023), 484-497.

Crossrefs

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

Row sums of A380166.

Formula

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