Matrix Representation of The Second Order Recurrence $\{u_{kn}\}$

Abstract

In this note, we consider a generalized Fibonacci sequence $\{u_n\}$. Then we give a generating matrix for the terms of sequence $\{u_{kn}\}$ for a positive integer $k$. With the aid of this matrix, we derive some new combinatorial identities for the sequence $\{u_{kn}\}$.