Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers

Abstract

In this study we define and study the Gaussian Jacob-sthal and Gaussian Jacobsthal Lucas numbers. We give generating functions, Binet formulas, explicit formulas and Q matrix of these numbers. We also present explicit combinatorial and determinantal expressions, study negatively subscripted numbers and give various identities. Similar to the Jacobsthal and Jacobsthal Lucas numbers we give some interesting results for the Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers.