Positive integer powers of certain complex tridiagonal matrices

摘要

In this paper, we firstly present a general expression for the entries of the rth (r∈N) power of a certain n-square complex tridiagonal matrix, in terms of the Chebyshev polynomials of the first kind. Secondly, we obtain a complex factorization formula for generalized Fibonacci–Pell numbers obeying also classical Fibonacci and Pell numbers.