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

Abstract

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.

Keywords

• Recurrence relation
• Determinant
• Tridiagonal k-Toeplitz matrices
• Chebyshev polynomials of second kind