The bi-periodic Horadam sequence and some perturbed tridiagonal 2-Toeplitz matrices: A unified approach

Heliyon. 2022 Feb 2;8(2):e08863. doi: 10.1016/j.heliyon.2022.e08863. eCollection 2022 Feb.

Abstract

In this note we consider the so-called bi-periodic Horadam sequences. Explicit formulas in terms of Chebyshev polynomials of the second kind and the determinant of some perturbed tridiagonal 2-Toeplitz matrices are established. Several illustrative examples are provided as well.

Keywords: Chebyshev polynomials of second kind; Determinant; Horadam sequence; Tridiagonal matrices.