A300131 Largest number of points that can be placed on an n X n point grid so that no point is equally distant from two other points on the same straight line.

1, 4, 6, 9, 16, 17, 21, 26, 31, 34, 40, 46

Offset: 1

Author

Heinrich Ludwig, Feb 26 2018

Keywords

• nonn
• hard
• more

Comments

This definition is a 2-dimensional generalization of A003002 ("no 3-term arithmetic progressions"). It generalizes the definition of A296468 to include not only triples on horizontal or vertical lines but on any straight line.

Examples

			On a 10 X 10 point grid 34 points (X) can be placed at most. Example:
  . X . . . X X . . .
  X X . . . X X . X .
  X . X X . . . . X .
  . . X . . . . X . X
  . . . . . . . . X X
  X X . . . . . . . .
  X . X . . . . X . .
  . X . . . . X X . X
  . X . X X . . . X X
  . . . X X . . . X .
		

Crossrefs

Cf. A003002, A296468.

Extensions

a(11) from Bert Dobbelaere, Jan 09 2020

a(12) from Bert Dobbelaere, Jan 12 2020