

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.


0




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



