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

Milica Anđelić; Carlos M da Fonseca; Fatih Yılmaz

doi:10.1016/j.heliyon.2022.e08863

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.

Authors

Milica Anđelić¹, Carlos M da Fonseca^{2

3}, Fatih Yılmaz⁴

Affiliations

¹ Department of Mathematics, Kuwait University, Safat 13060, Kuwait.
² Kuwait College of Science and Technology, Doha District, Safat 13133, Kuwait.
³ Chair of Computational Mathematics, University of Deusto, 48007 Bilbao, Spain.
⁴ Department of Mathematics, Ankara Hacı Bayram Veli University, Turkey.

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.