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On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences

Year 2019, Volume: 7 Issue: 2, 149 - 160, 15.10.2019
https://doi.org/10.36753/mathenot.588787

Abstract

In this paper, we consider Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas sequences. We introduce the quadra Fibona-Pell,Fibona-Jacobsthal and Pell-Jacobsthal and the hexa Fibona-Pell-Jacobsthal sequences whose components are the Fibonacci, Pell and Jacobsthal sequences. We derive the Binet-like formulas, the generating functions and the exponential generating functions of these sequences. Also, we obtain some binomial identities for them.

References

  • Cook C. K. and Bacon, M. R., Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations. In Annales Mathematicae et Informaticae Vol. 41 (2013), 27-39.
  • Fayeab B. and Lucab F., Pell and Pell-Lucas numbers with only one distinct digit. In Annales Mathematicae et Informaticae. Vol. 45 (2015), 55-60.
  • Harne, S. and Parihar, C. L., Some generalized Fibonacci polynomials. J. Indian Acad. Math. 18 (1996), no. 2, 251–253.
  • Harne, S. and Singh, B., Some properties of fourth-order recurrence relations. \emph{Vikram Math. J. } 20 (2000), 79–8
  • Horadam, A. F., Jacobsthal representation numbers. Fibonacci Quart. 34 (1996), no. 1, 40–54.
  • Kilic, E. and Tasci, D., On the families of bipartite graphs associated with sums of Fibonacci and Lucas numbers. Ars Combin. 89 (2008), 31-40.
  • Kilic, E. and Tasci, D., On the second order linear recurrences by tridiagonal matrices. Ars Combin. 91 (2009), 11–18 Koshy, T., Pell and Pell-Lucas numbers with applications. Springer, New York, 2014. Koshy, T., Fibonacci and Lucas Numbers with Applications Volume 1, John Wiley \& Sons, New Jersey, 2018. Koshy, T., Fibonacci and Lucas Numbers with Applications Volume 2, John Wiley \& Sons, New Jersey, 2019.
  • Lee, Gwang-Yeon k-Lucas numbers and associated bipartite graphs. Linear Algebra Appl. 320 (2000), no. 1-3, 51–61.
  • Minc, H., Permanents of (0,1)-circulants. Canad. Math. Bull. 7 (1964), 253–263.
  • Ozkoc, A., Some algebraic identities on quadra Fibona-Pell integer sequence, Adv. Difference Equ. 148 (2015), 10 p.
  • Sato, S., On matrix representations of generalized Fibonacci numbers and their applications, in Applications of Fibonacci Numbers, Vol. 5 (st. Andrews, 1992) (Kluwer Acad. Publ., Dordrecht, 1993), 487-496. Tasci, D., On quadrapell numbers and quadrapell polynomials. Hacet. J. Math. Stat. 38 (2009), no.3, 265-275. Kızılate\c{s}, C., On the Quadra Lucas-Jacobsthal Numbers. Karaelmas Science and Engineering Journal. 7(2) (2017), 619-621.
Year 2019, Volume: 7 Issue: 2, 149 - 160, 15.10.2019
https://doi.org/10.36753/mathenot.588787

Abstract

References

  • Cook C. K. and Bacon, M. R., Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations. In Annales Mathematicae et Informaticae Vol. 41 (2013), 27-39.
  • Fayeab B. and Lucab F., Pell and Pell-Lucas numbers with only one distinct digit. In Annales Mathematicae et Informaticae. Vol. 45 (2015), 55-60.
  • Harne, S. and Parihar, C. L., Some generalized Fibonacci polynomials. J. Indian Acad. Math. 18 (1996), no. 2, 251–253.
  • Harne, S. and Singh, B., Some properties of fourth-order recurrence relations. \emph{Vikram Math. J. } 20 (2000), 79–8
  • Horadam, A. F., Jacobsthal representation numbers. Fibonacci Quart. 34 (1996), no. 1, 40–54.
  • Kilic, E. and Tasci, D., On the families of bipartite graphs associated with sums of Fibonacci and Lucas numbers. Ars Combin. 89 (2008), 31-40.
  • Kilic, E. and Tasci, D., On the second order linear recurrences by tridiagonal matrices. Ars Combin. 91 (2009), 11–18 Koshy, T., Pell and Pell-Lucas numbers with applications. Springer, New York, 2014. Koshy, T., Fibonacci and Lucas Numbers with Applications Volume 1, John Wiley \& Sons, New Jersey, 2018. Koshy, T., Fibonacci and Lucas Numbers with Applications Volume 2, John Wiley \& Sons, New Jersey, 2019.
  • Lee, Gwang-Yeon k-Lucas numbers and associated bipartite graphs. Linear Algebra Appl. 320 (2000), no. 1-3, 51–61.
  • Minc, H., Permanents of (0,1)-circulants. Canad. Math. Bull. 7 (1964), 253–263.
  • Ozkoc, A., Some algebraic identities on quadra Fibona-Pell integer sequence, Adv. Difference Equ. 148 (2015), 10 p.
  • Sato, S., On matrix representations of generalized Fibonacci numbers and their applications, in Applications of Fibonacci Numbers, Vol. 5 (st. Andrews, 1992) (Kluwer Acad. Publ., Dordrecht, 1993), 487-496. Tasci, D., On quadrapell numbers and quadrapell polynomials. Hacet. J. Math. Stat. 38 (2009), no.3, 265-275. Kızılate\c{s}, C., On the Quadra Lucas-Jacobsthal Numbers. Karaelmas Science and Engineering Journal. 7(2) (2017), 619-621.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Hamza Menken 0000-0003-1194-3162

Orhan Dişkaya

Publication Date October 15, 2019
Submission Date July 8, 2019
Acceptance Date October 3, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Menken, H., & Dişkaya, O. (2019). On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences. Mathematical Sciences and Applications E-Notes, 7(2), 149-160. https://doi.org/10.36753/mathenot.588787
AMA Menken H, Dişkaya O. On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences. Math. Sci. Appl. E-Notes. October 2019;7(2):149-160. doi:10.36753/mathenot.588787
Chicago Menken, Hamza, and Orhan Dişkaya. “On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences”. Mathematical Sciences and Applications E-Notes 7, no. 2 (October 2019): 149-60. https://doi.org/10.36753/mathenot.588787.
EndNote Menken H, Dişkaya O (October 1, 2019) On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences. Mathematical Sciences and Applications E-Notes 7 2 149–160.
IEEE H. Menken and O. Dişkaya, “On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences”, Math. Sci. Appl. E-Notes, vol. 7, no. 2, pp. 149–160, 2019, doi: 10.36753/mathenot.588787.
ISNAD Menken, Hamza - Dişkaya, Orhan. “On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences”. Mathematical Sciences and Applications E-Notes 7/2 (October 2019), 149-160. https://doi.org/10.36753/mathenot.588787.
JAMA Menken H, Dişkaya O. On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences. Math. Sci. Appl. E-Notes. 2019;7:149–160.
MLA Menken, Hamza and Orhan Dişkaya. “On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 2, 2019, pp. 149-60, doi:10.36753/mathenot.588787.
Vancouver Menken H, Dişkaya O. On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences. Math. Sci. Appl. E-Notes. 2019;7(2):149-60.

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