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

Yıl 2019, Cilt: 7 Sayı: 2, 149 - 160, 15.10.2019

Hamza Menken Orhan Dişkaya

https://doi.org/10.36753/mathenot.588787

Cited By: 2

Öz

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.

Anahtar Kelimeler

Fibonacci sequence, Lucas sequence, Pell sequence, Jacobsthal sequence, Binet-like formula, generating function, exponential generating function

Kaynakça

• 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.