%I #27 Jan 21 2022 23:09:04
%S 1,4,9,15,22,28,36
%N 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.
%C The hexagon with side length n has n+1 points along each edge and contains a total of A003215(n) points.
%C The following lower bounds are known:
%C a(7) >= 44;
%C a(8) >= 52;
%C a(9) >= 60.
%C All currently known values and lower bounds can be achieved by a configuration with reflective symmetry.
%e For n = 4 the a(4) = 22 solution, unique up to rotation, is:
%e .
%e o x x o x
%e x x o o o x
%e x o o o o x o
%e o o o o o o x x
%e x o o o o o o o x
%e x x o o o o o o
%e o x o o o o x
%e x o o o x x
%e x o x x o
%e .
%Y Cf. A003215, A008893, A240114.
%K nonn,hard,more
%O 0,2
%A _Zachary DeStefano_, Jan 06 2022
