cp's OEIS Frontend

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.

%I A350547 #27 Jan 21 2022 23:09:04
%S A350547 1,4,9,15,22,28,36
%N 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.
%C A350547 The hexagon with side length n has n+1 points along each edge and contains a total of A003215(n) points.
%C A350547 The following lower bounds are known:
%C A350547 a(7) >= 44;
%C A350547 a(8) >= 52;
%C A350547 a(9) >= 60.
%C A350547 All currently known values and lower bounds can be achieved by a configuration with reflective symmetry.
%e A350547 For n = 4 the a(4) = 22 solution, unique up to rotation, is:
%e A350547 .
%e A350547       o x x o x
%e A350547      x x o o o x
%e A350547     x o o o o x o
%e A350547    o o o o o o x x
%e A350547   x o o o o o o o x
%e A350547    x x o o o o o o
%e A350547     o x o o o o x
%e A350547      x o o o x x
%e A350547       x o x x o
%e A350547 .
%Y A350547 Cf. A003215, A008893, A240114.
%K A350547 nonn,hard,more
%O A350547 0,2
%A A350547 _Zachary DeStefano_, Jan 06 2022