ON GENERALIZED SİXTH-ORDER PELL SEQUENCES

Yıl 2020, Cilt: 4 Sayı: 1, 49 - 70, 31.01.2020

Yüksel Soykan

https://doi.org/10.26900/jsp.4.005

Öz

In this paper, we investigate the generalized sixth order Pell sequences and we deal with, in detail, three special cases which we call them as sixth order Pell, sixth order Pell-Lucas and modified sixth order Pell sequences.

Anahtar Kelimeler

Pell numbers, sixth order Pell numbers, sixth order Pell-Lucas numbers, Hexanacci num- bers.

Kaynakça

• [1] Bicknell, N., A primer on the Pell sequence and related sequence, Fibonacci Quarterly, 13(4), 345-349, 1975.
• [2] Dasdemir, A., On the Pell, Pell-Lucas and Modi.ed Pell Numbers By Matrix Method, Applied Mathematical Sciences, 5(64), 3173-3181, 2011.
• [3] Ercolano, J., Matrix generator of Pell sequence, Fibonacci Quarterly, 17(1), 71-77, 1979.
• [4] Gökbas, H., Köse, H., Some sum formulas for products of Pell and Pell-Lucas numbers, Int. J. Adv. Appl. Math. and Mech. 4(4), 1-4, 2017.
• [5] Hanusa, C., A Generalized Binet.s Formula for kth Order Linear Recurrences: A Markov Chain Approach, Harvey Mudd College, Undergraduate Thesis (Math Senior Thesis), 2001.
• [6] Horadam, A. F., Pell identities, Fibonacci Quarterly, 9(3), 245-263, 1971.
• [7] Kalman, D., Generalized Fibonacci Numbers By Matrix Methods, Fibonacci Quarterly, 20(1), 73-76, 1982.
• [8] Kiliç, E., Ta¸sçi, D., The Linear Algebra of The Pell Matrix, Boletín de la Sociedad Matemática Mexicana, 3(11), 2005.
• [9] Kiliç, E., Ta¸sçi, D., The Generalized Binet Formula, Representation and Sums of the Generalized Order-k Pell Numbers, Taiwanese Journal of Mathematics, 10(6), 1661-1670, 2006.
• [10] Kiliç, E., Stanica, P., A Matrix Approach for General Higher Order Linear Recurrences, Bulletin of the Malaysian Mathe-matical Sciences Society, (2) 34(1), 51.67, 2011.
• [11] Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
• [12] Melham, R., Sums Involving Fibonacci and Pell Numbers, Portugaliae Mathematica, 56(3), 309-317, 1999.
• [13] N.J.A. Sloane, The on-line encyclopedia of integer sequences, http://oeis.org/
• [14] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, arXiv:1903.01313v1 [math.NT], 2019.
• [15] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 45-56, 2019.
• [16] Soykan, Y., On Generalized Third-Order Pell Numbers, Asian Journal of Advanced Research and Reports, 6(1): 1-18, 2019.
• [17] Soykan, Y., A Study of Generalized Fourth-Order Pell Sequences, Journal of Scienti.c Research and Reports, 25(1-2), 1-18, 2019.
• [18] Soykan, Y., Properties of Generalized Fifth-Order Pell Numbers, Asian Research Journal of Mathematics, 15(3), 1-18, 2019.
• [19] Ya¼gmur, T., New Approach to Pell and Pell-Lucas Sequences, Kyungpook Math. J. 59, 23-34,2019.