Jacobsthal-Leonardo Sequence, Some Identities and Summation Formulas

In this paper we introduce a particular number sequence, namely Jacobsthal-Leonardo sequence that is a combination of Jacobsthal sequence and Leonardo number. The Binet-likeformula, partial sum, generating function related to this sequence are represented. Cassini’s identity, other interesting identities and summation formulas about this sequence are stated. Furthermore, some examples related to these identities are given. Finally, we give a PYTHONcode to generate the first 𝑛 terms of Jacobsthal-Leonardo sequence.

Keywords:

Jacobsthal sequence , Leonardo number , Binet Formula , Summation formula .