Generalized Gaussian Fibonacci numbers and sums by matrix methods

Abstract

Many authors define certain generalizations of the usual Fibonacci, Pell and Lucas numbers by matrix methods and then obtain the Binet formulas and combinatorial representations of the generalizations of these number sequence. In this article firstly we define and study the generalized Gaussian Fibonacci numbers and then find the matrix representation of positively and negatively subscripted terms of generalized Gaussian Fibonacci numbers and prove some theorems by these matrix representations. We also find the sums of generalized Gaussian Fibonacci numbers by matrix method.