Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers

2011/11/10 by Kaygisiz, Kenan, Sahin, Adem
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1111.2567

Abstract

In this paper, we present a new generalization of the Lucas numbers by matrix representation using Genaralized Lucas Polynomials. We give some properties of this new generalization and some relations between the generalized order-k Lucas numbers and generalized order-k Fibonacci numbers. In addition, we obtain Binet formula and combinatorial representation for generalized order-k Lucas numbers by using properties of generalized Fibonacci numbers.

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