On the Padovan sequence

Abstract

The aim of this article is to give some properties of the so-called Padovan sequence $(T_n{)}_{n\ge 0}$ defined by $$T_{n+3}=T_{n+1}+T_n\forall n\in \mathbb{N},T_1=T_2=T_3=1$$ that is divisibility properties, periods, identities.