Determinants of circulant matrices with Gaussian Nickel Fibonacci numbers

In this study, we consider 7Cn := circ (GN1, GN2, ... , GNn) circulant matrices whose entries are the Gaussian Nickel Fibonacci numbers GN1, GN2, ... , GNn. Then, we compute determinants of 7Cn by exploiting Chebyshev polynomials of the second kind. Moreover, we obtain Cassini's identity and the D'Ocagne identity for the Gaussian Nickel Fibonacci numbers.