@article{Katırcı2026, 
author = {Tuba Çakmak Katırcı and Can Alçelik},
title = {On the Lucas-Leonardo numbers in complex and dual-complex number systems},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {915-942},
keywords = {complex numbers, complex Lucas-Leonardo numbers, dual-complex numbers, dual-complex Lucas-Leonardo numbers},
url = {https://www.sciopen.com/article/10.3934/math.2026040},
doi = {10.3934/math.2026040},
abstract = {This study aimed to introduce the Lucas-Leonardo numbers in 2-dimensional real algebra and 4-dimensional real Clifford algebra, namely, complex and dual-complex Lucas-Leonardo numbers, respectively. In this sense, basic algebraic properties of these numbers were presented as well as some Fibonacci-type identities such as Cassini, Catalan, and d'Ocagne. The generating function and Binet formula were constructed for the complex and dual-complex forms of Lucas-Leonardo numbers. Some relations between these numbers and other well-known integer sequences were proven. Moreover, some formulas related to the sums of the terms of these sequences were established.}
}