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

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.

On the constant coefficients of a certain recurrence relation: A simple proof.

In this note, we provide a short proof for the explicit formulas of the coefficients of a particular 3-term recurrence relation derived from a k-periodic recurrence. Any of the recurrences can be naturally interpreted in terms of determinants of Hessenberg matrices families.

Comment on "Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs".

In this Comment we recall the notion of a tridiagonal 2-Toeplitz matrix and its spectrum, confronting these results with others obtained recently on exact solutions of thermal transport in dimerized harmonic lattices.