On the difference equation

In this paper we study the behavior of the solutions of the difference equation where α is a negative number. Included are results which considerably improve and correct those in the recently published paper: [A.E. Hamza, On the recursive sequence , J. Math. Anal. Appl. 322 (2006), 668–674]. We also refute Conjecture 2 in [G. Ladas, Open problems and conjectures, J. Difference. Equ. Appl. 7 (2) (2001), 477–482].