涉及广义Fibonacci和Lucas数的组合恒等式

The New Multiple Sums on the Generalized Fibonacci and Lucas Numbers

研究了二阶常系数线性齐次递归序列,利用发生函数和积分的方法,通过比较关于发生函数的恒等式左右两端的系数,建立了一系列涉及广义Fibonacci和Lucas数的多重和的组合恒等式.

By considering two order constant coefficient homogeneous linear recurrent sequences,and using the method of generating function and integration,the coefficients of identities on both sides are compared and several multiple sums of new forms for the generalized Fibonacci and Lucas numbers are established.