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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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,more,tabl
AUTHOR
N. J. A. Sloane, following a tip from Ed Pegg Jr, May 28 2005
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)