

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



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



