On the limit of a recurrence relation

In this paper we study the asymptotic properties of the sequence of integer s g(n), defined by the following recurrence relation: g(n + 1) = [(1 + alpha/n-alpha)g(n)], where alpha > 0 and [x] denotes the largest integer not greater than x. For any alpha > 0, the limit g(n)/n(alpha) exists. We prove that for alpha = 2 , this limit is always rational. For alpha = 3, we give some sufficient con ditions which guarantee that the limit is rational.