A296994 Largest number of points that can be selected from an n X n X n triangular point grid so that no selected point is equally distant from two other selected points on a straight line, which is parallel to one side of the grid.

1, 3, 4, 7, 10, 14, 18, 20, 23, 27, 31, 36, 42, 48, 54, 61, 68, 76, 84, 92, 98

Offset: 1

Author

Heinrich Ludwig, Mar 26 2018

Keywords

• nonn
• nice
• hard
• more

Comments

This sequence generalizes the idea of A003002 ("no 3-term arithmetic progressions") for triangular point grids.

For the same idea applied to square grids see A296468 and A300131.

Examples

			At most 54 points (X) can be chosen from a 15 X 15 X 15 triangular point grid under the condition mentioned above. Example:
                 o
                X X
               X o X
              o X X o
             X X o X X
            X o o o o X
           o o X o X o o
          o o o o o o o o
         o o X X o X X o o
        o X o o X X o o X o
       X X o o X o X o o X X
      X o X X o o o o X X o X
     o X X o o X o X o o X X o
    X X o X X o o o o X X o X X
   X o o o o X X o X X o o o o X
		

Crossrefs

Cf. A296468, A300131.

Extensions

a(20) from Heinrich Ludwig, Apr 24 2018

a(21) from Heinrich Ludwig, May 01 2018