I've been thinking for about 2 months at a problem and I haven't manage to find a solution, so I've decided to ask for your help. The problem is pretty nice. It asks for the number of trees(2 trees are considered different if they are not isomorphs) with N vertices and diameter D. Here you have the link . It was given in Polish Algorithmic Engagements 2008 at the final round and as far as I know there are no written solutions for this kind of contest.