Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21289320240901Some new families of generalized $k$-Leonardo and Gaussian Leonardo Numbers5395531454410.22049/cco.2023.28236.1485ENKalikaPrasadDepartment of Mathematics, Central University of Jharkhand, India, 8352050000-0002-3653-5854RitanjaliMohantyDepartment of Mathematics, Central University of Jharkhand, India, 8352050000-0002-5885-5613MuneshKumariDepartment of Mathematics, Central University of Jharkhand, India, 8352050000-0002-6541-0284HrishikeshMahatoDepartment of Mathematics, Central University of Jharkhand, India, 8352050000-0002-3769-0653Journal Article20230109In this paper, we introduce a new family of the generalized $k$-Leonardo numbers and study their properties. We investigate the Gaussian Leonardo numbers and associated new families of these Gaussian forms. We obtain combinatorial identities like Binet formula, Cassini's identity, partial sum, etc. in the closed form. Moreover, we give various generating and exponential generating functions.http://comb-opt.azaruniv.ac.ir/article_14544_6844cc9ba641d31cafe5358297bc0096.pdf