Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences

In this paper, we consider a generalization of Horadam sequence {wn} which is defined by the recurrence relation wn=chi (n)wn-1+cwn-2, where chi (n)=a if n is even, chi (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 the 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 a matrix approach.