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A351700 T(n,k) is the maximum number of points that can be chosen from a rectangle of n X k lattice points such that their mutual distances are distinct, where T(n,k) is a triangle read by rows, 1 <= k <= n.

%I A351700 #28 Jul 14 2022 02:33:18
%S A351700 1,2,2,2,3,3,3,4,4,4,3,4,4,5,5,3,4,5,5,5,6,4,5,5,6,6,6,7,4,5,5,6,7,7,
%T A351700 7,7,4,5,6,6,7,7,8,8,8,4,6,6,7,7,8,8,8,9,9,4,6,6,7,8,8,8,9,9,9,10,5,6,
%U A351700 7,7,8,9,9,9,9,10,10,10,5,6,7,8,8,9,9,10,10,10,10,11,11
%N A351700 T(n,k) is the maximum number of points that can be chosen from a rectangle of n X k lattice points such that their mutual distances are distinct, where T(n,k) is a triangle read by rows, 1 <= k <= n.
%H A351700 Fausto A. C. Cariboni, <a href="/A351700/b351700.txt">Rows n = 1..16, flattened</a>
%e A351700 The triangle begins:
%e A351700   1
%e A351700   2  2
%e A351700   2  3  3
%e A351700   3  4  4  4
%e A351700   3  4  4  5  5
%e A351700   3  4  5  5  5  6
%e A351700   4  5  5  6  6  6  7
%e A351700   4  5  5  6  7  7  7  7
%e A351700   4  5  6  6  7  7  8  8  8
%e A351700   4  6  6  7  7  8  8  8  9  9
%e A351700   4  6  6  7  8  8  8  9  9  9 10
%e A351700   5  6  7  7  8  9  9  9  9 10 10 10
%e A351700   5  6  7  8  8  9  9 10 10 10 10 11 11
%Y A351700 First occurrence of n in first column: A227590.
%Y A351700 Main diagonal: A271490.
%Y A351700 Cf. A003022, A193838, A351699.
%K A351700 nonn,tabl,hard
%O A351700 1,2
%A A351700 _Hugo Pfoertner_, Mar 05 2022
%E A351700 T(13,2)=a(80) and T(13,8)=a(86) corrected by _Fausto A. C. Cariboni_, Jul 10 2022