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http://dx.doi.org/10.5666/KMJ.2019.59.1.23

New Approach to Pell and Pell-Lucas Sequences  

Yagmur, Tulay (Department of Mathematics, Aksaray University)
Publication Information
Kyungpook Mathematical Journal / v.59, no.1, 2019 , pp. 23-34 More about this Journal
Abstract
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 $p_0=2$, $p_1=2a$, respectively. We give generating functions and Binet's formulas for these sequences. Also, we obtain some identities of these sequences.
Keywords
Pell sequence; Pell-Lucas sequence;
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