A381865 Number of sequences in which the matches of a fully symmetric single-elimination tournament with 3^n players can be played if arbitrarily many matches can occur simultaneously and each match involves 3 players.

1, 1, 13, 308682013, 20447648974223714249697186722386536049691073

Offset: 0

Author

Noah A Rosenberg, Mar 08 2025

Keywords

• nonn
• more

Comments

a(n) is also the number of tie-permitting labeled histories for a fully symmetric strictly trifurcating labeled topology with 3^n leaves.

Examples

			Two of the 13 cases with n=2 and 3^2=9 players are: (1) (A,B,C) play, then (D,E,F) play, then (G,H,I) play, then the winners of the three matches play; (2) (A,B,C) play simultaneously with (D,E,F), then the winners of these two matches play against G, then the winner plays against H and I.
		

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=3)

Crossrefs

Cf. A273723 (if matches must be non-simultaneous), A379758 (if matches involve only two players at a time).