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 \(\{u_{kn}\}\).