Determinants of Circulant Matrices with Gaussian Nickel Fibonacci Numbers

Abstract

In this study, we consider $\mathcal{K}_{n}:=\mbox{circ}\,(GN_{1},GN_{2},\ldots ,GN_{n})$ circulant matrices whose entries are the Gaussian Nickel Fibonacci numbers $GN_{1},GN_{2},\ldots ,GN_{n}$. Then, we compute determinants of $\mathcal{K}_{n}$ by exploiting the set of orthogonal polynomial, Chebyshev polynomials of the second kind. Moreover, we obtain Cassini's identity and the D'Ocagne identity for the Gaussian Nickel Fibonacci numbers.