A350547 Maximum size of a set of points taken from a hexagonal section of a hexagonal grid with side length n such that no three selected points form an equilateral triangle.

1, 4, 9, 15, 22, 28, 36

Offset: 0

Author

Zachary DeStefano, Jan 06 2022

Keywords

• nonn
• hard
• more

Comments

The hexagon with side length n has n+1 points along each edge and contains a total of A003215(n) points.

The following lower bounds are known:

a(7) >= 44;

a(8) >= 52;

a(9) >= 60.

All currently known values and lower bounds can be achieved by a configuration with reflective symmetry.

Examples

			For n = 4 the a(4) = 22 solution, unique up to rotation, is:
.
      o x x o x
     x x o o o x
    x o o o o x o
   o o o o o o x x
  x o o o o o o o x
   x x o o o o o o
    o x o o o o x
     x o o o x x
      x o x x o
.
		

Crossrefs

Cf. A003215, A008893, A240114.