A381948 Number of sequences in which the matches of a fully symmetric single-elimination tournament with 4^n players can be played if arbitrarily many matches can occur simultaneously and each match involves 4 players.

1, 1, 75, 3016718788056802445, 940214577272785072764883853635996915471902343186386048409875362373502134253520788722829230121857323681047351543536731036815

Offset: 0

Author

Noah A Rosenberg, Mar 10 2025

Keywords

• nonn

Comments

a(n) is also the number of tie-permitting labeled histories for a fully symmetric strictly quadfurcating labeled topology with 4^n leaves.

Examples

			Two of the 75 cases with n=4 and 4^2=16 players are: (1) (A,B,C,D) play, then (E,F,G,H) play, then (I,J,K,L) play, then (M,N,O,P) play, then the winners of the four matches play; (2) (A,B,C,D) play simultaneously with (E,F,G,H) and (I,J,K,L), then the winners of these three matches play against M, then the winner plays against N, O, and P.
		

Links

• Emily H. Dickey and Noah A. Rosenberg, Labelled histories with multifurcation and simultaneity, Phil. Trans. R. Soc. B 380 (2025), 20230307. (see Theorem 15 with r=4)

Crossrefs

Cf. A273725 (if matches must be non-simultaneous), A379758 (if matches involve only two players at a time), A381865 (if matches involve only three players at a time).