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In this paper, we consider a generalization of Horadam sequence fwng which isdefined by the recurrence relation wn = x(n)wn-1+ cwn-2; where x(n) = a if n iseven, x(n) = b if n is odd with arbitrary initial conditions w0;w1 and nonzeroreal numbers a, b and c. As a special case, by taking initial conditions 0, 1and 2, b we define the sequences {un} and {vn}, respectively. The main purposeof this study is to derive some basic properties of the sequences {un}, {vn}and {wn} by using matrix approach.

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