On the sequence made by the linear combination of k-Fibonacci and k-Lucas sequences

2016/06/27 by Kyunghwan Song, Youngwoo Kwon, Song, Kyunghwan +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #11B39 #11B75 #Advanced Mathematical Theories and Applications #Chaos control and synchronization #FOS: Mathematics #Fractal and DNA sequence analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1606.08152

openalex publication_date 2016/06/27 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28

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 S_k,n with initial conditions S_k,0 = 2b and S_k,1 = bk + a, which is generated by the recurrence relation S_k,n = kS_k,n-1 +Sk,n-2 for n >= 2, where a, b, k are real numbers. Using the sequence S_k,n, we introduce and prove some special identities. Also, we deal with the circulant and skew circulant matrices for the sequence S_k,n.

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