This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A240114 #55 Nov 21 2022 09:39:42 %S A240114 1,2,4,6,8,10,12,14,17,20,22,25,28,31,34 %N 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. %C A240114 Placing points on a triangular grid of side n, there are A000332(n + 3) triangles to be avoided. %C A240114 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, ... %C A240114 From _Elijah Beregovsky_, Nov 20 2022: (Start) %C A240114 a(n) >= 3n-11. %C A240114 This lower bound is given by the construction seen in the example section. %C A240114 Conjecture: for n >= 11, a(n) = 3n-11. (End) %e A240114 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. %e A240114 X %e A240114 . . %e A240114 . X . %e A240114 X . X . %e A240114 . X . . X %e A240114 X . . . X . %e A240114 . X . . . . X %e A240114 X . . . . . X . %e A240114 . X . . . . . . X %e A240114 X . . . . . . . X . %e A240114 . X . . . . . . . . X %e A240114 X . . . . . . . . . X . %e A240114 . X . . . . . . . . . . X %e A240114 . . . . . . . . . . . . X . %e A240114 . . X X X X X X X X X X X . . %Y A240114 Cf. A227308, A227116, A227133, A000332. %K A240114 nonn,nice,hard,more %O A240114 1,2 %A A240114 _Heinrich Ludwig_, Apr 01 2014 %E A240114 a(14) from _Heinrich Ludwig_, Jun 20 2014 %E A240114 a(15) from _Heinrich Ludwig_, Jun 21 2016