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