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

0,3

Comments

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

Links

Table of n, a(n) for n=0..4.

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)

Example

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.

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).

Sequence in context: A003745 A301468 A068942 * A116234 A065669 A367605

Adjacent sequences: A381945 A381946 A381947 * A381949 A381950 A381951

Keyword

nonn

Author

Noah A Rosenberg, Mar 10 2025

Status

approved