The (3, 3)-Type Equation xn+1 = α+βxn+γxn−1 A+Bxn+Cxn−1

Please recall our classification convention in which all coefficients of this equation are now assumed to be positive and the initial conditions nonnegative.

This equation has not been investigated yet. Here we make some simple observations about linearized stability, invariant intervals, and the convergence of solutions in certain regions of initial conditions.