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.
Original entry on oeis.org
1, 3, 365, 1323338487, 1119556146543237253601352961, 3414445659328795239581367793706562556567987857578516541118092297328702035
Offset: 1
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.
Cf.
A056972 (game sequences with only one arena).
A380767
Number of sequences in which the games of a single-elimination tournament with n teams can be played if arbitrarily many arenas are available and the tournament bracket is chosen to be the bracket with the largest such number of sequences.
Original entry on oeis.org
1, 1, 3, 5, 19, 63, 365, 1199, 7177, 36209, 295355, 1652085, 15193115, 114570449, 1323338487, 8732267521, 93577466255, 822198823101, 10952623368043
Offset: 2
For 5 teams A, B, C, D, E, the maximizing tournament structure is ((A,B),((C,D),E)). The 5 game sequences enumerated are: (1) Game (A,B), then game (C,D), then game ((C,D),E), then game ((A,B),((C,D),E)); (2) Game (C,D), then game (A,B), then game ((C,D),E), then game ((A,B),((C,D),E)); (3) Game (C,D), then game ((C,D),E), then game (A,B), then game ((A,B),((C,D),E)); (4) Game (A,B) and game (C,D) simultaneously, then game ((C,D),E), then game ((A,B),((C,D),E)); (5) Game (C,D), then game (A,B) and game ((C,D),E) simultaneously, then game ((A,B),((C,D),E)).
Cf.
A379758 and
A380166 for game sequences with fully symmetric tournaments.
A378855
Triangle read by rows: T(n,k) is the number of sequences in which the games of a single-elimination tournament with n teams can be played if arbitrarily many arenas are available, the tournament bracket is chosen to the bracket with the largest such number of sequences, and the number of distinct times at which games are played is k, log_2(n) <= k <= n-1.
Original entry on oeis.org
1, 0, 1, 0, 1, 2, 0, 0, 2, 3, 0, 0, 2, 9, 8, 0, 0, 1, 12, 30, 20, 0, 0, 1, 22, 102, 160, 80, 0, 0, 0, 10, 114, 380, 485, 210, 0, 0, 0, 10, 198, 1100, 2495, 2478, 896, 0, 0, 0, 5, 204, 1930, 7260, 12810, 10640, 3360, 0, 0, 0, 5, 344, 4890, 27110, 72702
Offset: 2
Triangle begins:
1;
0, 1;
0, 1, 2;
0, 0, 2, 3;
0, 0, 2, 9, 8;
0, 0, 1, 12, 30, 20;
0, 0, 1, 22, 102, 160, 80;
0, 0, 0, 10, 114, 380, 485, 210;
0, 0, 0, 10, 198, 1100, 2495, 2478, 896;
0, 0, 0, 5, 204, 1930, 7260, 12810, 10640, 3360;
0, 0, 0, 5, 344, 4890, 27110, 72702, 101024, 70080, 19200;
0, 0, 0, 2, 278, 6360, 53000, 211365, 451164, 529116, 321600, 79200;
Cf.
A380166 for the triangle if n is a power of 2.
Showing 1-3 of 3 results.
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