三阶Fibonacci数列的性质与应用

On the Property and the Application of Third Order Fibonacci Sequence

运用矩阵方法,对三阶Fibonacci数列进行了较深入的研究。求得了三阶Fibonacci数列的通项公式的多种表示法,并得到了一些与Fibonacci数列相似的性质,如与Cassini公式相似的三阶Cassini公式等。同时也涉及了三阶Fibonacci数列的运用问题。

With the application of matrix method, an intensive research on third order Fibonacci sequence is conducted to acquire a variety of representations of the general term formula of third order Fibonacci sequence and its associated similar properties such as third order Cassini formula, The application of third order Fibonacci sequence is also involved.