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

doi:10.1016/j.amc.2007.07.016

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	On the k-generalized Fibonacci numbers and high-order linear recurrence relations
	Yang, Sheng-liang
	2008-03-01
发表期刊	Applied Mathematics and Computation
ISSN	00963003
卷号	196 期号:2 页码:850-857
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.
关键词	Computation theory Functions Problem solving Companion matrix Elementary symmetric function Fibonacci sequence Linear homogeneous recurrence relation
DOI	10.1016/j.amc.2007.07.016
收录类别	EI ; SCIE
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000253631700036
出版者	Elsevier Inc., 360 Park Avenue South, New York, NY 10010, United States
EI入藏号	20080611082441
EI主题词	Linear programming
EI分类号	721.1 Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory - 723.1 Computer Programming - 723.4 Artificial Intelligence - 921 Mathematics
来源库	Compendex
分类代码	721.1 Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory - 723.1 Computer Programming - 723.4 Artificial Intelligence - 921 Mathematics
引用统计	被引频次：11[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://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
第一作者单位	理学院
第一作者的第一单位	理学院
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.