On the rational difference equation yn+1=A+yn-kyn

We find conditions for the global asymptotic stability, periodicity and semi-cycle analysis of the unique positive equilibrium y¯=1+A of the equationyn+1=A+yn-kyn,n=0,1,…where y−k, y−k+1, …, y0, A ∈ (0, ∞) and k ∈ {2, 3, 4, …}.