KöMaL 2005 A372

An equilateral triangle of side $n$ is divided into equilateral triangles of unit side. How many castles can be placed on the lattice points of the triangular lattice obtained so that no two of them attack each other? Castles can move parallel to the sides of the triangle, in six directions altogether. (Suggested by A. Egri, Hajdúszoboszló)