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K次Fibonacci数列{F_n^k}中连续K+2个数的线性递推关系 被引量:2

The linear recursion of continuous k+2 numbers in the k-times sequence of Fibonacci number {F_n^k}
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摘要 探讨了K次Fibonacci数列{Fnk}中连续的k+2个数之间的线性递推关系,并证明了对任意正整数k,Fnk+k+1必可以由其前面连续的k+1个数,Fkn,Fnk+1,……,Fnk+k线性表示,并给出了具体的求法。 This paper analyses the linear recursion relationship among the k + 2 numbers in the ktimes sequence of Fibonacci number,and proves that Fn+k+1^k can be represented by the previous con such tinuous k + 1 numbers for any positive interger k, such as Fn^k,Fn+1^k,……,Fn+k^k. It also gives some concrete solutions.
作者 陈逢明
出处 《福建工程学院学报》 CAS 2007年第3期297-300,共4页 Journal of Fujian University of Technology
基金 福建商业高等专科学校基金资助项目(D200710)
关键词 FIBONACCI数列 矩阵 初等变换 sequence of Fibonacci number matrix rank elementary transformation
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