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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

%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

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Last modified March 1 06:29 EST 2024. Contains 370430 sequences. (Running on oeis4.)