Determinants of some Hessenberg matrices with generating functions

Abstract

In this paper, we derive some relationships between the determinants of some special lower Hessenberg matrices whose entries are the terms of certain sequences and the generating functions of these sequences. Moreover, our results are generalizations of the earlier results from previous researches. Furthermore, interesting examples of the determinants of some special lower Hessenberg matrices are presented.

The Generating Function of a Bi-Periodic Leonardo Sequence

“…The reader is also invited to read [13] for an earlier look and historical context and [15] for other extensions. Note that we assume k < .…”