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A240114 Maximal number of points that can be placed on a triangular grid of side n so that no three of them are vertices of an equilateral triangle in any orientation. 4
1, 2, 4, 6, 8, 10, 12, 14, 17, 20, 22, 25, 28, 31, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Placing points on a triangular grid of side n, there are A000332(n + 3) triangles to be avoided.

The number k(n) of maximal solutions (reflections and rotations not counted) varies greatly: k(n) = 1, 1, 1, 1, 1, 3, 13, 129, 15, 2, 63, 3, 20, 1, ...

LINKS

Table of n, a(n) for n=1..15.

EXAMPLE

On a triangular grid of side 15, 34 points (X) can be placed so that no three of them form an equilateral triangle, regardless of its orientation.

                   X

                  . .

                 . X .

                X . X .

               . X . . X

              X . . . X .

             . X . . . . X

            X . . . . . X .

           . X . . . . . . X

          X . . . . . . . X .

         . X . . . . . . . . X

        X . . . . . . . . . X .

       . X . . . . . . . . . . X

      . . . . . . . . . . . . X .

     . . X X X X X X X X X X X . .

CROSSREFS

Cf. A227308, A227116, A227133, A000332.

Sequence in context: A063459 A186329 A062417 * A076828 A276106 A321501

Adjacent sequences:  A240111 A240112 A240113 * A240115 A240116 A240117

KEYWORD

nonn,nice,hard,more

AUTHOR

Heinrich Ludwig, Apr 01 2014

EXTENSIONS

a(14) from Heinrich Ludwig, Jun 20 2014

a(15) from Heinrich Ludwig, Jun 21 2016

STATUS

approved

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)