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Some special number sequences obtained from a difference equation of degree three

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  • Flaut, Cristina
  • Savin, Diana

Abstract

In this paper we present applications of special numbers obtained from a difference equation of degree three. As a particular case of this difference equation of degree three, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were extended to the generalized quaternion algebras. Using properties of these quaternion elements, we can define a set with an interesting algebraic structure, namely, an order on a generalized rational quaternion algebra. Another presented application is in the Coding Theory, since some of these numbers can be used to built cyclic codes with good properties (MDS codes).

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  • Flaut, Cristina & Savin, Diana, 2018. "Some special number sequences obtained from a difference equation of degree three," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 67-71.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:67-71
    DOI: 10.1016/j.chaos.2017.11.015
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    References listed on IDEAS

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    1. Basu, Manjusri & Prasad, Bandhu, 2009. "The generalized relations among the code elements for Fibonacci coding theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2517-2525.
    2. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    3. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
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    Cited by:

    1. Flaut, Cristina & Savin, Diana, 2019. "Some remarks regarding l-elements defined in algebras obtained by the Cayley–Dickson process," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 112-116.
    2. Florek, Wojciech, 2018. "A class of generalized Tribonacci sequences applied to counting problems," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 809-821.

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