A107431 Triangle read by rows: T(n,k) = maximal number of rounds for the social golfer problem with n groups of k golfers (n >= 2, 2 <= k <= n).

3, 5, 4, 7, 4, 5, 9, 7, 5, 6, 11, 8, 7, 6, 3, 13, 10, 9

Offset

2,1

Comments

The problem is to find the largest number of rounds of golf that can be arranged with n*k golfers who play in n groups of k. No golfer may play in the same group as any other golfer twice (i.e., maximum socialisation is achieved).

T(6,6) cannot be 4 since this would be equivalent to a pair of mutually orthogonal Latin squares of order 6.

T(n,k) = 1 for values of n and k outside this range.

The next term T(7,5) is known to be either 7 or 8.

T(n,n) = A001438(n) + 2. - Floris P. van Doorn, Sep 05 2019

Links

Table of n, a(n) for n=2..19.

W. Harvey, Results Page for the Social Golfer Problem

Floris P. van Doorn, Dagstuhl's Happy Diner Problem - Latin Squares

Example

Triangle begins:
   3;
   5, 4;
   7, 4, 5;
   9, 7, 5, 6;
  11, 8, 7, 6, 3;
  ...
T(2,2) = 3 from { 12/34, 13/24, 14/23 }.

Crossrefs

Column 3 gives A107432.

Cf. A001438.

Sequence in context: A094761 A114748 A182733 * A189827 A023859 A096457

Adjacent sequences: A107428 A107429 A107430 * A107432 A107433 A107434

Keyword

nonn,more,tabl

Author

N. J. A. Sloane, following a tip from Ed Pegg Jr, May 28 2005

Status

approved