Generalized (p,q)-Fibonacci-Like Sequences and Their Properties

摘要

In this paper, we define the generalized (p,q) -Fibonacci-Like sequences Sp,q,n associated with the (p,q) -Fibonacci and the (p,q) -Lucas sequences and then we get some fundamental identities and sums formulas involving odd and even terms of the generalized (p,q) -Fibonacci-Like sequences. We obtain the Binet's formula to find the n th general term of generalized (p,q) -Fibonacci-Like sequences Sp,q,n . Also, the generating functions of these sequences are presented and proved.In this paper, we define the generalized (p,q) -Fibonacci-Like sequences Sp,q,n associated with the (p,q) -Fibonacci and the (p,q) -Lucas sequences and then we get some fundamental identities and sums formulas involving odd and even terms of the generalized (p,q) -Fibonacci-Like sequences. We obtain the Binet's formula to find the n th general term of generalized (p,q) -Fibonacci-Like sequences Sp,q,n . Also, the generating functions of these sequences are presented and proved.