Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences
Abstract
In this paper, we consider a generalization of Horadam sequence fwng which is defined by the recurrence relation wn = x(n)wn-1+ cwn-2; where x(n) = a if n is even, x(n) = b if n is odd with arbitrary initial conditions w0;w1 and nonzero real numbers a, b and c. As a special case, by taking initial conditions 0, 1 and 2, b we define the sequences un and vn, respectively. The main purpose of this study is to derive some basic properties of the sequences un, vn and wn by using matrix approach.
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