Fibonacci-k序列通项公式的矩阵证明方法

A Proof of the General Term of the Fibonacci-k Series Using the Matrix

给出了Fibonacci序列的一种推广,称为Fibonacci-k序列,利用Fibonacci-k序列的递推关系,构造了Fibonacci-k相伴矩阵Qk,证明了第n个Fibonacci-k数可以用Qk的k个特征值进行表示.

In this paper, a generalization of the series { Fn^（k）}. Using the recursion relationship of the series is established. The n-th the Fibonacci-k number Fibonacci series is given, which is called the Fibonacci-k Fibonacci-k series, the adjoint matrix Qk of the Fibonacci-k is proven, which can be expressed by the eigenvalues of Qk.