cp's OEIS Frontend

A274332 Team size n for which there exists a balanced tournament for 2n+1 players so that in 2n+1 matches each player plays exactly n-1 times with and n times against each other player.

%I A274332 #36 Nov 04 2018 01:27:49
%S A274332 1,2,3,5,6,8,9,11,14,15,18,20,21,23,26,29,30,33
%N A274332 Team size n for which there exists a balanced tournament for 2n+1 players so that in 2n+1 matches each player plays exactly n-1 times with and n times against each other player.
%C A274332 There are 2n+1 players and 2n+1 matches. In each match one person rests, and the remaining 2n players are divided into two equal teams.
%C A274332 Up to n=33 there is probably only a unique design (up to permutation), and it has point / mirror symmetry.
%C A274332 It is conjectured that this sequence is identical to A005097 (ref. Kohen link).
%C A274332 a(n) = A130290(n+2) = A102781(n+2) = A139791(n+1) = A005097(n+1) for 0 <= n <= 17. - _Georg Fischer_, Oct 30 2018
%H A274332 Daniel Kohen and Ivan Sadofschi, <a href="http://arxiv.org/abs/1006.2571">A New Approach on the Seating Couples Problem</a>, arXiv:1006.2571 [math.CO], 2010.
%F A274332 Conjectured design scheme for Team 1 (N:= 2n+1; here players count from 0..2n): X, X+1 (mod N), X+1+2 (mod N), X+1+2+3 (mod N), ...; X = 0..2n (match number). Resting player: (X + (n*(n+1)/2) (mod N).
%e A274332 n=5:
%e A274332 Match 1: 1,2,3,5,8 versus 4,7,9,10,11
%e A274332 Match 2: 2,3,4,6,9 versus 5,8,10,11,1
%e A274332 Matches 3..11: further cyclic permutations
%Y A274332 Cf. A005097, A102781, A130290, A139791.
%K A274332 nonn,more
%O A274332 0,2
%A A274332 _Michael Steyer_, Jun 22 2016