De Moivre-type identities for the Jacobsthal numbers

The main aim of this study is to obtain De Moivre-type identities for Jacobsthal numbers. Also, this paper presents a method for constructing the second order Jacobsthal and Jacobsthal third-order numbers and the third-order Jacobsthal and Jacobsthal-Lucas numbers. Moreover, we give some interesting identities, such as Binet's formulas for some specific third-order Jacobsthal numbers that we derive from De Moivre-type identities.