New Approach to Pell and Pell-Lucas Sequences

In this paper, we first define generalizations of Pell and Pell-Lucas sequences by the recurrence relations p(n) = 2ap(n-1) + (b - a(2))p(n-2) and q(n) = 2aq(n-1) + (b - a(2))q(n-2) with initial conditions p(0) = 0, p(1) = 1, and q(0) = 2, q(1) = 2a, respectively. We give generating functions and Binet's formulas for these sequences. Also, we obtain some identities of these sequences.