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arXiv · 1111.2567

Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers

Kenan Kaygisiz·Adem Sahin
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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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Kenan Kaygisiz, Adem Sahin. 2011-11-10. Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers. https://arxiv.org/abs/1111.2567

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