A New Generalization of Jacobsthal Lucas Numbers (Bi-Periodic Jacobsthal Lucas Sequence)
Sukran Uygun *
Department of Mathematics, Faculty of Science and Arts, Gaziantep University, Gaziantep, Turkey.
Evans Owusu
Department of Mathematics, Faculty of Science and Arts, Gaziantep University, Gaziantep, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this study, we bring into light a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as
with initial conditions $$\ \hat{c}_{0}=2,\ \hat{c}_{1}=a.$$
The Binet formula as well as the generating function for this sequence are given. The convergence property of the consecutive terms of this sequence is examined after which the well known Cassini, Catalan and the D'ocagne identities as well as some related summation formulas are also given.
Keywords: Bi-periodic Jacobsthal sequence, Jacobsthal Lucas sequence, Generalized Jacobsthal Lucas sequence, Generating function, Binet formula