A note on the recursive sequence xn+1 = pkxn + pk-1xn-1+...+ p1xn-k+1

Abstract

We present some comments on the behavior of solutions of the difference equation xn+1 = pkxn + pk-1xn-1 + ... + p1xn-k+1, n = - 1, 0, 1, ..., where pi ≥ 0, i = 1, ..., k, k ∈ N, and x-k,..., x-1 ∈ R.