Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions - Ünal, Zafer (Black Sea Journal of Engineering and Science, 2023)
Fibonacci and Lucas numbers have been the most popular integer sequences since they were defined. These integer sequences have many uses, from nature to computer science, from art to financial analysis. Many researchers have worked on this subject. Sedenions form a 16-dimensional algebra on the field of real numbers. Various systems can be constructed by using the terms of special integer sequences instead of terms in sedenions. In this study, we define dual Fibonacci (DFS) and dual Lucas sedenions (DLS) with the help of Fibonacci and Lucas termed sedenions. Then we calculate some special identities for DFS and DLS such as Vajda's, Catalan's, d'Ocagne's, Cassini's.
Keywords: Engineering; Mühendislik; Fibonacci and Lucas numbers; Dual numbers; Sedenions; Vajda’s identity; Binet-like formula