Yilmaz, Cigdemigdem zeynepSacli, Gulsum yeliz2026-04-042026-04-0420241225-293X2288-6176https://doi.org/10.5831/HMJ.2024.46.4.677https://hdl.handle.net/11411/10739In this study, we introduce a new generalization of the Leonardo sequence, dual quaternions with the DGC Leonardo sequence coefficients, depending on the parameter p is an element of R. This generalization gives dual quaternions with the dual-complex Leonardo sequence for p = -1, dual quaternions with the hyper-dual Leonardo sequence for p = 0, and dual quaternions with the dual-hyperbolic Leonardo sequence for p = 1. The basic algebraic structures and some special characteristic relations are presented, as well as the Binet's formula, generating function, d'Ocagne's, Catalan's, Cassini's, and Tagiuri's identities.eninfo:eu-repo/semantics/closedAccessLeonardo SequenceDual QuaternionDual-Generalized Complex NumberRecurrence RelationHttpsArticle10.5831/HMJ.2024.46.4.67710.5831/HMJ.2024.46.4.677696467746Q4WOS:001415827400012