This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381948 #10 Mar 19 2025 10:27:57 %S A381948 1,1,75,3016718788056802445, %T A381948 940214577272785072764883853635996915471902343186386048409875362373502134253520788722829230121857323681047351543536731036815 %N 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. %C A381948 a(n) is also the number of tie-permitting labeled histories for a fully symmetric strictly quadfurcating labeled topology with 4^n leaves. %H A381948 Emily H. Dickey and Noah A. Rosenberg, <a href="https://doi.org/10.1098/rstb.2023.0307">Labelled histories with multifurcation and simultaneity</a>, Phil. Trans. R. Soc. B 380 (2025), 20230307. (see Theorem 15 with r=4) %e A381948 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. %Y A381948 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). %K A381948 nonn %O A381948 0,3 %A A381948 _Noah A Rosenberg_, Mar 10 2025