TY - JOUR
ID - 14544
TI - Some new families of generalized $k$-Leonardo and Gaussian Leonardo Numbers
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Prasad, Kalika
AU - Mohanty, Ritanjali
AU - Kumari, Munesh
AU - Mahato, Hrishikesh
AD - Department of Mathematics, Central University of Jharkhand, India, 835205
Y1 - 2024
PY - 2024
VL - 9
IS - 3
SP - 539
EP - 553
KW - k-Leonardo numbers
KW - k-Gaussian Leonardo numbers
KW - Binet formula
KW - Generating functions
KW - Partial sum
DO - 10.22049/cco.2023.28236.1485
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_14544.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14544_6844cc9ba641d31cafe5358297bc0096.pdf
ER -