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Some identities of the generalized Fibonacci and Lucas sequences

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  • Yang, Jizhen
  • Zhang, Zhizheng

Abstract

The purpose of this paper is to study generalized Fibonacci and Lucas sequences. We first introduce generalized Lucas sequences. Section 2 contains a list of elementary relationships about generalized Fibonacci and Lucas sequences. In Section 3, we give a generalization of the Binet’s formulas of generalized Fibonacci, Lucas sequences and its applications. Section 4 is devote to derive many identities and congruence relations for generalized Fibonacci, Lucas sequences by using operator method.

Suggested Citation

  • Yang, Jizhen & Zhang, Zhizheng, 2018. "Some identities of the generalized Fibonacci and Lucas sequences," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 451-458.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:451-458
    DOI: 10.1016/j.amc.2018.07.054
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    References listed on IDEAS

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    1. Ye, Xiaoli & Zhang, Zhizheng, 2017. "A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 31-37.
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    Cited by:

    1. Ilija Tanackov & Ivan Pavkov & Željko Stević, 2020. "The New New-Nacci Method for Calculating the Roots of a Univariate Polynomial and Solution of Quintic Equation in Radicals," Mathematics, MDPI, vol. 8(5), pages 1-18, May.

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