On r-Jacobsthal and r-Jacobsthal-Lucas Numbers

Abstract

Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate r-Jacobsthal–Lucas sequence for the r-Jacobsthal sequence, we obtain some properties of these two sequences. For simpler results, we define two new sequences and examine their properties, too. Finally, we generalize some well-known identities.

Keywords

• r-jacobsthal numbers
• r-jacobsthal–lucas numbers
• binet formula
• 11b83
• 11b37