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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
1, 4, 9, 15, 22, 28, 36 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 16 03:04 EDT 2022. Contains 353687 sequences. (Running on oeis4.)