Pentanacci and Pentanacci-Lucas hybrid numbers

Işbilir, Zehra; Gürses, Nurten

doi:10.1080/09720529.2021.1936899

Open Access A

Pentanacci and Pentanacci-Lucas hybrid numbers

Zehra Işbilirzehraisbilir@duzce.edu.trDepartment of Mathematics Faculty of Arts and Sciences Düzce University 81620 Düzce TurkeyDüzce, 81620, TürkiyeView full profile → , ^*Nurten GürsesCorresponding authornbayrak@yildiz.edu.trDepartment of Mathematics Faculty of Arts and Sciences Yildiz Technical University 34220 Istanbul TurkeyDepartment of Mathematics Faculty of Arts and Sciences Yildiz Technical UniversityIstanbul, 34220, TürkiyeView full profile →

* Corresponding author · click or hover a name for details

pp. 423–442Vol. 26Issue 2March 2022DOI: 10.1080/09720529.2021.1936899 Crossmark XML

Received:: 01 Nov 2020
Accepted:: 05 Mar 2021
Published Online:: 15 Nov 2021
Article type:: A
Language:: EN
Article no.:: JDMSC-1358
Pages:: 423–442

Abstract

The aim of this study is to introduce the Pentanacci and Pentanacci-Lucas hybrid numbers. Then, some properties with respect to these special numbers and relations between them are obtained. In addition, matrix formulations, generating functions, Binet- like formulas and some summation formulas of them are examined.

Keywords

Pentanacci numbers Pentanacci-Lucas numbers Hybrid numbers Pentanacci hybrid numbers Pentanacci-Lucas hybrid numbers

Subject Classifications

(2010) 11B3711C2011K31

References

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Views: 137Downloads: 9Citations: 2

[1] F. E. Barros, F. R. V. Alves, M. C. dos S. Mangueira, R. P. M. Vieira and P. M. M. C. Catarino, Hibridização dos números triangulares: uma análise preliminar e a priori e a visualização por meio do software GeoGebra, Indagatio Didactica, 12(3), (2020), 411-435. DOI: https://doi.org/10.34624/id.v12i3.20106 [Google Scholar]

[2] P. M. M. C. Catarino, On k-Pell hybrid numbers, J. Discret. Math. Sci. Cryptogr., 22(1), (2019), 83-89. DOI: https://doi.org/10.1080/09720529.2019.1569822 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

[3] G. Cerda-Morales, Investigation of generalized Fibonacci hybrid numbers and their properties, Applied Mathematics E-Notes, 21, (2021), 110-118. [Web of Science ®], [Google Scholar]

[4] G. Dattoli, S. Licciardi, R. M. Pidatella and E. Sabia, Hybrid complex numbers: the matrix version, Adv. Appl. Clifford Algebras, 28(3), Article number: 58, (2018). DOI: https://doi.org/10.1007/s00006-018-0870-y [Crossref], [Web of Science ®], [Google Scholar]

[5] G. P. B. Dresden and Z. Du, A simplified Binet formula for k-generalized Fibonacci numbers, J. Integer Seq., 17(4), (2014). [Google Scholar]

[6] R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific, Singapore, (1997). DOI: https://doi.org/10.1142/3595 [Crossref], [Google Scholar]

[7] D. Kalman, Generalized Fibonacci numbers by matrix methods, Fibonacci Q., 20(1), (1982), 73-76. [Web of Science ®], [Google Scholar]

[8] A. M. Karakaş and M. Karakaş, A new BK-space defined by regular matrix of Lucas numbers, J. Interdiscip. Math., 22(6), 837-847, (2019). DOI: https://doi.org/10.1080/09720502.2019.1668152 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

[9] C. Kızılateş, A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons & Fractals, 130, 109449, (2020). DOI: https://doi.org/10.1016/j.chaos.2019.109449 [PubMed], [Google Scholar]

[10] C. Kızılateş, A note on Horadam hybrinomials, Preprints, (2020). DOI: https://doi.org/10.20944/preprints202001.0116.v1 [Google Scholar]

[11] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Inc., New York, (2001). DOI: https://doi.org/10.1002/9781118033067 [Crossref], [Google Scholar]

[12] T. Koshy, Fibonacci and Lucas Numbers with Applications Volume 2, John Wiley and Sons, Inc., New York, (2019). DOI: https://doi.org/10.1002/9781118742297 [Google Scholar]

[13] T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer, New York, (2014). DOI: https://doi.org/10.1007/978-1-4614-8489-9 [Crossref], [Google Scholar]

[14] M. C. dos S. Mangueira, F. R. V. Alves and P. M. M. C. Catarino, Números híbridos de Mersenne, C.Q.D-Revista Eletrônica Paulista de Matemática, 18, (2020). DOI: https://doi.org/10.21167/cqdvol18ic202023169664mcsmfrvapmmcc0111 [Google Scholar]

[15] M. C. dos S. Mangueira, R. P. M. Vieira, F. R. V. Alves and P. M. M. C. Catarino, The hybrid numbers of Padovan and some identities, Ann. Math. Sil., 34(2), (2020), 256–267. DOI: https://doi.org/10.2478/amsil-2020-0019 [Crossref], [Google Scholar]

[16] M. Özdemir, Introduction to hybrid numbers, Adv. Appl. Clifford Algebras, 28(1), Article number: 11, (2018). DOI: https://doi.org/10.1007/s00006-018-0833-3 [Crossref], [Web of Science ®],

Journal of Discrete Mathematical Sciences and Cryptography

Pentanacci and Pentanacci-Lucas hybrid numbers

Abstract

Keywords

Subject Classifications

References