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2022 | 36 (2) | 129--150
Tytuł artykułu

On Quaternion Gaussian Bronze Fibonacci Numbers

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet's formula, generating function and certain properties and identities are provided. Tridiagonal matrices are considered to determine the general term of this sequence.(original abstract)
Słowa kluczowe
Rocznik
Tom
Strony
129--150
Opis fizyczny
Twórcy
  • University of Trás-os-Montes e Alto Douro Portugal
  • University of Trás-os-Montes e Alto Douro Portugal
Bibliografia
  • Akyiǧit M., Kösal H.H., and Tosun M., Split Fibonacci quaternions, Adv. Appl. Clifford Algebr. 23 (2013), no. 3, 535-545.
  • Asci M. and Gurel E., Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers, Ars Combin. 111 (2013), 53-63.
  • Berzsenyi G., Gaussian Fibonacci numbers, Fibonacci Quart. 15 (1977), no. 3, 233-236.
  • Bilgici G. and Catarino P., Unrestricted Pell and Pell-Lucas quaternions, Int. J. Math. Syst. Sci. 1 (2018), no. 3, Article ID: 816, 4 pp.
  • Catarino P., The modified Pell and the modified k-Pell quaternions and octonions, Adv. Appl. Clifford Algebr. 26 (2016), no. 2, 577-590.
  • Catarino P., Bicomplex k-Pell quaternions, Comput. Methods Funct. Theory 19 (2019), no. 1, 65-76.
  • Catarino P., On k-Pell hybrid numbers, J. Discrete Math. Sci. Cryptogr. 22 (2019), no. 1, 83-89.
  • Catarino P., and A. Borges, A note on incomplete Leonardo numbers, Integers 20 (2020), Paper No. A43, 7 pp.
  • Catarino P., and A. Borges, On Leonardo numbers, Acta Math. Univ. Comenian. (N.S.) 89 (2020), no. 1, 75-86.
  • Catarino P., and H. Campos, A note on Gaussian modified Pell numbers, J. Inf. Optim. Sci. 39 (2018), no. 6, 1363-1371.
  • Catarino P., and P. Vasco, The generalized order-m (k-Pell) numbers, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 66 (2020), no. 1, 55-65.
  • Choo Y., A generalized quaternion with generalized Fibonacci number components, Appl. Math. Sci. 14 (2020), no. 1, 31-38.
  • Falcon S., On the generating matrices of the k-Fibonacci numbers, Proyecciones 32 (2013), no. 4, 347-357.
  • Halici S., On quaternion-Gaussian Lucas numbers, Math. Methods Appl. Sci. 44 (2021), no. 9, 7601-7606.
  • Halici S. and Cerda-Morales G., On quaternion-Gaussian Fibonacci numbers and their properties, An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat. 29 (2021), no. 1, 71-82.
  • Halici S. and Karataş A., On a generalization for Fibonacci quaternions, Chaos Solitons Fractals 98 (2017), 178-182.
  • Halici S. and Öz S., On some Gaussian Pell and Pell-Lucas numbers, Ordu Univ. J. Sci. Tech. 6 (2016), no. 1, 8-18.
  • Hamilton W.R., Elements of Quaternions, Longmans, Green, & Co., London, 1866.
  • Horadam A.F., Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly 70 (1963), 289-291.
  • Huang L. and So W., Quadratic formulas for quaternions, Appl. Math. Lett. 15 (2002), no. 5, 533-540.
  • Jordan J.H., Gaussian Fibonacci and Lucas numbers, Fibonacci Quart. 3 (1965), 315-318.
  • Kartal M.Y., Gaussian Bronze Fibonacci numbers, EJONS Int. J. Math. Eng. Nat. Sci. 4 (2020), no. 13, 19-25.
  • Kılıç E. and Tasci D., On the generalized Fibonacci and Pell sequences by Hessenberg matrices, Ars Combin. 94 (2010), 161-174.
  • Kılıç E., Tasci D., and Haukkanen P., On the generalized Lucas sequences by Hessenberg matrices, Ars Combin. 95 (2010), 383-395.
  • Kızılateş C., A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos Solitons Fractals 130 (2020), 109449, 5 pp.
  • Koshy T., Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
  • Levesque C., On m-th order linear recurrences, Fibonacci Quart. 23 (1985), no. 4, 290-293.
  • Polatli E., Kizilates C., and Kesim S., On split k-Fibonacci and k-Lucas quaternions, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 353-362.
  • Sloane N.J.A., The On-Line Encyclopedia of Integer Sequences, The OEIS Foundation Inc., http://oeis.org/.
  • Synge J.L., Quaternions, Lorentz Transformations, and the Conway-Dirac-Eddington Matrices, Communications of the Dublin Institute for Advanced Studies, Series A, 21, Dublin Inst. for Adv. Stud., Dublin, 1972.
  • Szynal-Liana A. and Włoch I., A note on Jacobsthal quaternions, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 441-447.
  • Tasci D., On k-Jacobsthal and k-Jacobsthal-Lucas quaternions, J. Sci. Arts 40 (2017), no. 3, 469-476.
  • Tokeşer Ü., Ünal Z., and Bilgici G., Split Pell and Pell-Lucas quaternions, Adv. Appl. Clifford Algebr. 27 (2017), no. 2, 1881-1893.
  • Yaǧmur T., Split Jacobsthal and Jacobsthal-Lucas quaternions, Commun. Math. Appl. 10 (2019), no. 3, 429-438.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ekon-element-000171653482

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