On the sequence made by the linear combination of k-Fibonacci and k-Lucas sequences
Abstract
The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the new sequence Sk,n with initial conditions Sk,0 = 2b and Sk,1 = bk + a, which is generated by the recurrence relation Sk,n = kSk,n-1 +Sk,n-2 for n >= 2, where a, b, k are real numbers. Using the sequence Sk,n, we introduce and prove some special identities. Also, we deal with the circulant and skew circulant matrices for the sequence Sk,n.
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