MEMO 2014 I2

We consider dissections of regular $n$ -gons into $n - 2$ triangles by $n - 3$ diagonals which do not intersect inside the $n$ -gon. A bicoloured triangulation is such a dissection of an $n$ -gon in which each triangle is coloured black or white and any two triangles which share an edge have different colours. We call a positive integer $n \ge 4$ triangulable if every regular $n$ -gon has a bicoloured triangulation such that for each vertex $A$ of the $n$ -gon the number of black triangles of which $A$ is a vertex is greater than the number of white triangles of which $A$ is a vertex.

Find all triangulable numbers.