On the sequence made by the linear combination of k-Fibonacci and k-Lucas sequences
Number Theory
2017-05-31 v3
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} +S{k,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}.
Keywords
Cite
@article{arxiv.1606.08152,
title = {On the sequence made by the linear combination of k-Fibonacci and k-Lucas sequences},
author = {Kyunghwan Song and Youngwoo Kwon},
journal= {arXiv preprint arXiv:1606.08152},
year = {2017}
}
Comments
This paper has been withdrawn by the author due to some improved results were made by co-authors