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.

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, 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, 7, 7, 8, 9, 9, 9, 9, 10, 10, 10, 5, 6, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11

Offset: 1

Author

Hugo Pfoertner, Mar 05 2022

Keywords

• nonn
• tabl
• hard

Examples

			The triangle begins:
  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  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  7  7  8  9  9  9  9 10 10 10
  5  6  7  8  8  9  9 10 10 10 10 11 11
		

Links

• Fausto A. C. Cariboni, Rows n = 1..16, flattened

Crossrefs

First occurrence of n in first column: A227590.

Main diagonal: A271490.

Cf. A003022, A193838, A351699.

Extensions

T(13,2)=a(80) and T(13,8)=a(86) corrected by Fausto A. C. Cariboni, Jul 10 2022