On a sequence derived from the Laplace transform of the characteristic polynomial of the Fibonacci sequence

Abstract

Recently, based on the Laplace transform of the characteristic polynomial of the Fibonacci sequence, Deveci and Shannon established a new sequence and analysed some of its properties. They disclosed in particular the odd terms. In this short note, we provide a matricial representation for this sequence as well as one in terms of the Chebyshev polynomials of the second kind. The subsequence of the even terms is also disclosed.