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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 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

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Last modified August 4 16:34 EDT 2020. Contains 336202 sequences. (Running on oeis4.)