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Generalized hyper-Lucas numbers and applications

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Abstract

In this paper, we give some combinatorial properties of a new generalization of hyper-Lucas numbers in order to extend the Cassini determinant. We also study norms of some circulant and s-circulant matrices.

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References

  1. L. Ait-Amrane and D. Behloul, Cassini determinant involving new generalized hyper-Fibonacci numbers, submited.

  2. L. Ait-Amrane and D. Behloul, Cassini determinant involving the \((a,b)\)-hyper-Fibonacci numbers, Malaya J. Mat. 8 (2020), no. 3, 939–944.

    Article  MathSciNet  Google Scholar 

  3. M. Bahşī  and S. Solak, On the norms of \(r\)-circulant matrices with the hyper-Fibonacci and Lucas numbers, J. Math. Inequal. 8 (4) (2014), 693–705.

    Article  MathSciNet  Google Scholar 

  4. H. Belbachir and F. Bencherif, Linear recurrent sequences and powers of a square matrix. Integers. 6 (2006), A12, 17 pp.

  5. N. N. Cao and F. Z. Zhao, Some properties of hyperfibonacci and hyperlucas numbers. J. Integer Seq. 13 (8) (2010), Article 10.8.8, 11 pp.

  6. P. J. Davis, Circulant Matrices, Wiley, New York, Chichester, Brisbane, 1979.

    MATH  Google Scholar 

  7. A. Dil and I. Mező, A symmetric algorithm for hyperharmonic and Fibonacci numbers. Appl. Math. Comput. 206 (2) (2008), 942–951.

    MathSciNet  MATH  Google Scholar 

  8. C. Köme and Y. Yazlik, On the spectral norms of  \(r\)-circulant matrices with the biperiodic Fibonacci and Lucas numbers. J. Inequal. Appl. (2017), Paper No. 192, 12 pp.

  9. C. Krattenthaler and A. M. Oller-Marcén, A determinant of generalized Fibonacci numbers. J. Comb. Number Theory. 5 (2) (2013), 95–102.

    MathSciNet  MATH  Google Scholar 

  10. I. Martinjak and I. Urbiha, A new generalized Cassini determinant. Colloquium Mathematicum. 145 (2) (2016), 209–218.

    MathSciNet  MATH  Google Scholar 

  11. E. P. Miles, Jr., Generalized Fibonacci numbers and associated matrices, Amer. Math. Monthly. 67 (1960), 745–752.

    Article  MathSciNet  Google Scholar 

  12. S. Shen and J. Cen, On the bounds for the norms of  \(r\)-circulant matrices with the Fibonacci and Lucas numbers, Appl. Math. Comp. 216 (10) (2010), 2891–2897.

    Article  MathSciNet  Google Scholar 

  13. A. P. Stakhov, Fibonacci matrices, a generalization of the "Cassini formula", and a new coding theory. Chaos Solitons Fractals. 30 (1) (2006), 56–66.

    Article  MathSciNet  Google Scholar 

  14. N. G. Voll, The Cassini identity and its relatives. Fibonacci Quart. 48 (3) (2010), 197–201.

    MathSciNet  MATH  Google Scholar 

  15. Y. Yazlik and N. Taskara, On the norms of an  \(r\)-circulant matrix with the generalized  \(k\)-Horadam numbers. J. Inequal. Appl. (2013), 2013:394, 8 pp.

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Correspondence to Lyes Ait-Amrane.

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Communicated by B. Sury.

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Ait-Amrane, L., Behloul, D. Generalized hyper-Lucas numbers and applications. Indian J Pure Appl Math 53, 62–75 (2022). https://doi.org/10.1007/s13226-021-00013-y

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  • DOI: https://doi.org/10.1007/s13226-021-00013-y

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