k-Oresme Numbers and k-Oresme Numbers with Negative Indices

Abstract

In this study, we gave some properties and identities for k-Oresme numbers which is a generalization of well-known number sequence called Oresme numbers. We considered and analyzed the k-Oresme numbers with negative indices. By defining the generating matrix of these numbers and using some matrix and determinant properties, we deduced some important identities. We also examined the sums of alternating, odd and even terms of k-Oresme numbers and sums of negative-indexed k-Oresme numbers. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.