On the difference equation xn=xn-kb+cxn-1⋯xn-k

摘要

We describe the behavior of well-defined solutions of the difference equationxn=xn-kb+cxn-1⋯xn-k,n∈N0,where k∈N, parameters b, c and the initial values x−k, … , x−1 are real numbers. These results, among others, improve and extend our results in [S. Stević, More on a rational recurrence relation, Appl. Math. E-Notes 4 (2004) 80–85].