OFFSET
0,2
COMMENTS
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.
Up to n=33 there is probably only a unique design (up to permutation), and it has point / mirror symmetry.
It is conjectured that this sequence is identical to A005097 (ref. Kohen link).
a(n) = A130290(n+2) = A102781(n+2) = A139791(n+1) = A005097(n+1) for 0 <= n <= 17. - Georg Fischer, Oct 30 2018
LINKS
Daniel Kohen and Ivan Sadofschi, A New Approach on the Seating Couples Problem, arXiv:1006.2571 [math.CO], 2010.
FORMULA
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).
EXAMPLE
n=5:
Match 1: 1,2,3,5,8 versus 4,7,9,10,11
Match 2: 2,3,4,6,9 versus 5,8,10,11,1
Matches 3..11: further cyclic permutations
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Michael Steyer, Jun 22 2016
STATUS
approved