IMO 1976 SL 4

Problem

(GBR 1a)IMO6 For all positive integral n, un+1 = un(u2 n−1 −2) −u1, u0 = 2, and u1 = 5/2. Prove that 3 log2[un] = 2n −(−1)n, where [x] is the integral part of x.