On Various Binomial Transforms of the Generalized Pell Matrix Sequences

The main aim of this study is to apply different binomial transforms to the generalized Pell matrix sequences. We define the binomial, $s$-binomial, rising, and falling transforms for the generalized Pell matrix sequence. We establish some algebraic properties, such as the recurrent formulas, Binet formulas, generating functions, and sum formulas, for binomial transforms of the generalized Pell matrix sequences. Finally, we discuss the need for further research.