On $k$-generalized Lucas sequence with its triangle

Authors: ABDULLAH AÇIKEL, AMROUCHE SAID, HACENE BELBACHIR, NURETTİN IRMAK

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 $s \in \mathbb{N}.$

Keywords: $k-$generalized Lucas sequence, arithmetic triangle, recurrence relation, bi$^s$nomial coefficient

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