Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers
Number Theory
2011-11-11 v1
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.
Cite
@article{arxiv.1111.2567,
title = {Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers},
author = {Kenan Kaygisiz and Adem Sahin},
journal= {arXiv preprint arXiv:1111.2567},
year = {2011}
}