We investigate the behavior of the solutions of the recursive sequence x(n+1) = alpha + x(n-1)/x(n)(k), n = 0,1,..., where alpha is an element of [0,infinity), k is an element of (0,infinity), and the initial conditions x(-1), x(0) are arbitrary positive numbers. Included are results that considerably improve those in the recently published paper by Hamza and Morsy (2009).