一种新的二阶线性递推多项式及其应用

A New Second-Order Linear Recurrence Polynomials and Some Applications

构造了一种新的二阶线性递推多项式,利用初等方法和组合技巧研究其性质,并得到一些有趣的恒等式.同时,作为所得定理的重要应用,给出一些关于Fibonacci数列、Lucas数列、Pell数列的恒等式.

In this paper,we introduced a new second-order linear recurrence polynomials,then used the elementary method and the combinational skills to study its various properties,and obtained some interesting identities.As some important applications of our results,we gave several new identities involving the famous Fibonacci numbers,Lucas numbers,Pell numbers.