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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 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.)