New Identities for Padovan Numbers

Abstract

In \cite{Choi-Jo}, the $am+b$ ($0\le b<a$) subscripted Tribonacci numbers are studied. This work is devoted to study a new generalization of Fibonacci numbers called Padovan numbers. In particular, the $am+b$ subscripted Padovan numbers will be expressed by three $a$ step apart Padovan numbers for any $0\le b<a$, where $a\in \mathbb{Z}$.