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

1,2

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.

Links

Table of n, a(n) for n=1..21.

Example

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.

Sequence in context: A287410 A228643 A304066 * A236475 A287458 A050572

Adjacent sequences: A296991 A296992 A296993 * A296995 A296996 A296997

Keyword

nonn,nice,hard,more

Author

Heinrich Ludwig, Mar 26 2018

Extensions

a(20) from Heinrich Ludwig, Apr 24 2018

a(21) from Heinrich Ludwig, May 01 2018

Status

approved