

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
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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



