%0 Journal Article
%T Some new families of generalized $k$-Leonardo and Gaussian Leonardo Numbers
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Prasad, Kalika
%A Mohanty, Ritanjali
%A Kumari, Munesh
%A Mahato, Hrishikesh
%D 2024
%\ 09/01/2024
%V 9
%N 3
%P 539-553
%! Some new families of generalized $k$-Leonardo and Gaussian Leonardo Numbers
%K k-Leonardo numbers
%K k-Gaussian Leonardo numbers
%K Binet formula
%K Generating functions
%K Partial sum
%R 10.22049/cco.2023.28236.1485
%X In 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.
%U http://comb-opt.azaruniv.ac.ir/article_14544_6844cc9ba641d31cafe5358297bc0096.pdf