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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. 5
 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, ... From Elijah Beregovsky, Nov 20 2022: (Start) a(n) >= 3n-11. This lower bound is given by the construction seen in the example section. Conjecture: for n >= 11, a(n) = 3n-11. (End) 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 September 25 11:40 EDT 2023. Contains 365644 sequences. (Running on oeis4.)