D.H. Lehmer's Tridiagonal determinant: An Etude in (Andrews-Inspired) Experimental Mathematics

TL;DR

This paper employs a reverse engineering approach inspired by George Andrews to derive explicit formulas for the determinant of a specific finite tridiagonal matrix, extending Lehmer's original infinite case analysis and connecting to OEIS sequence A039924.

Contribution

It introduces a novel explicit expression for the finite case determinant of Lehmer's tridiagonal matrix, bridging finite and infinite cases through experimental mathematics.

Findings

Derived explicit formula for finite case determinant

Connected finite case results to OEIS sequence A039924

Extended Lehmer's infinite case to finite matrices

Abstract

We use a "reverse engineering" method, pioneered by George Andrews, to discover an explicit expression for the determinant of a certain tridiagonal matrix discussed by Derrick Henry Lehmer in 1974, that lead to OEIS sequence A039924. Lehmer only did the infinite case, and here we also do the finite case, that immediately implies the former by taking the limit as n goes to infinity