On $k$-generalized Lucas sequence with its triangle

Abstract

In this paper, we investigate several identities of $k$-generalized Lucas numbers with $k$-generalized Fibonacci numbers. We also establish a link between generalized $s$-Lucas triangle and bi$^{s}$nomial coefficients given by the coefficients of the development of a power of $(1+x+x^{2}+\cdots+x^{s}),$ with $s \in \mathbb{N}.$