On r-Jacobsthal and r-Jacobsthal-Lucas Numbers - Bilgici, Göksal; Bród, Dorota (Walter de Gruyter GmbH, 2023)
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–lucas numbers; b37; b83; \(r\)-Jacobsthal numbers; r-jacobsthal numbers; QA1-939; Fibonacci and Lucas numbers and polynomials and generalizations; binet formula; \(r\)-Jacobsthal-Lucas numbers; Binet formula; Mathematics