Two dimensional Gaussian Pell sequences

Abstract

"In this study firstly we carried out the Pell sequence to the complex plane, then we defined the sequence into two dimensions. We called this generalized sequence two dimensional gaussian Pell sequence. We investigated the Binet formula, generating function, sum formula, explicit closed formula, and some relations between Pell sequences. Also, we get a matrix equality for obtaining elements of the two-dimensional gaussian Pell sequence. "