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

0,2

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.

Links

Table of n, a(n) for n=0..6.

Example

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.

Sequence in context: A066495 A313298 A313299 * A055999 A134227 A022945

Adjacent sequences: A350544 A350545 A350546 * A350548 A350549 A350550

Keyword

nonn,hard,more

Author

Zachary DeStefano, Jan 06 2022

Status

approved