摘要
研究了k-k型广义Fibonacci数列{Rn}:Rn+1=kRn+kRn-1,R0=R1=1,利用它的递推关系和特征方程得到了它的两个通项表达式,同时还运用{Rn}的递推性质,采用初等方法获得了{Rn}的与Fibonacci数列相似的两个性质和5个求和公式,推广了2-2型广义Fibonacci数列的相关结论。
The k-k generalized Fibonacci sequence{Rn}：Rn＋1=kRn＋kRn-1,R0=R1=1, was investigated. Two general expressions of the generalized Fibonacci sequence {Rn} were obtained from its recursion relations and the eigen equation. Meanwhile, two properties and five summation formulas of {Rn}, which were similar to those of Fibonacci sequence, were also obtained by using recursive properties of {Rn } with elementary methods. The conclusion of 2-2 pattern generalized Fibonacci sequence was verified.
出处
《海军工程大学学报》
CAS
北大核心
2012年第6期48-52,共5页
Journal of Naval University of Engineering
基金
海南省自然科学基金资助项目(110004)
