The 𝒏th Power of Generalized (𝒔, 𝒕)-Jacobsthal and (𝒔, 𝒕)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties

Abstract

In this study, new formulas for the 𝑛th power of (𝑠, 𝑡)-Jacobsthal and (𝑠, 𝑡)-Jacobsthal Lucas special matrix sequences are established by using determinant and trace of the matrices. By these formulas, some identities for (𝑠, 𝑡)-Jacobsthal and (𝑠, 𝑡)-Jacobsthal Lucas sequences are obtained. The formulas for finding the 𝑛th power for classic Jacobsthal and Jacobsthal Lucas matrix sequences are also derivable if we choose 𝑠 = 𝑡 = 1.