Pell polynomials of some rings of order p^2 and their periods

In this paper, the sequences of the Pell polynomials are obtained according to modulo m where x^2=2x+1 and various properties of these sequences are introduced. It is shown that these sequences are periodic and their periods are obtained. It is defined the Pell polynomials to the ring of complex numbers. Also, the Pell Polynomial-type orbits P_((α,β))^R (x)={x_i } are defined where R be a 2-generator ring and (α,β) is a generating pair of the ring R. The Pell Polynomial-type orbits P_((α,β))^R (x) in finite 2-generator rings of order p^2 are obtained and their periods are introduced.