On the k-generalized Fibonacci numbers and high-order linear recurrence relations

doi:10.1016/j.amc.2007.07.016

CORC > 兰州理工大学 > 兰州理工大学 > 理学院

	On the k-generalized Fibonacci numbers and high-order linear recurrence relations
	Yang, Sheng-liang
刊名	Applied Mathematics and Computation
	2008-03-01
卷号	196 期号:2 页码:850-857
关键词	Computation theory Functions Problem solving Companion matrix Elementary symmetric function Fibonacci sequence Linear homogeneous recurrence relation
ISSN号	00963003
DOI	10.1016/j.amc.2007.07.016
英文摘要	In this paper, using elementary symmetric function and complete homogeneous symmetric function, we obtain a determinant formula for the k-generalized Fibonacci sequence. The relationship between the k-generalized Fibonacci sequence and the order-k linear homogeneous recurrence relation has been investigated, and a general solution for the latter is also derived. Furthermore, we obtain an explicit expression for the elements in the nth power of the companion matrix in terms of k-generalized Fibonacci numbers. © 2007 Elsevier Inc. All rights reserved.
WOS研究方向	Mathematics
语种	英语
出版者	Elsevier Inc., 360 Park Avenue South, New York, NY 10010, United States
WOS记录号	WOS:000253631700036
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/111858]
专题	理学院
作者单位	Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
推荐引用方式 GB/T 7714	Yang, Sheng-liang. On the k-generalized Fibonacci numbers and high-order linear recurrence relations[J]. Applied Mathematics and Computation,2008,196(2):850-857.
APA	Yang, Sheng-liang.(2008).On the k-generalized Fibonacci numbers and high-order linear recurrence relations.Applied Mathematics and Computation,196(2),850-857.
MLA	Yang, Sheng-liang."On the k-generalized Fibonacci numbers and high-order linear recurrence relations".Applied Mathematics and Computation 196.2(2008):850-857.