Properties of Generalized Fifth-Order Pell Numbers

Main Article Content

Yüksel Soykan


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

Pell numbers, fifth order Pell numbers, fifth order Pell-Lucas numbers.

Article Details

How to Cite
Soykan, Y. (2019). Properties of Generalized Fifth-Order Pell Numbers. Asian Research Journal of Mathematics, 15(3), 1-18.
Original Research Article


Melham RS. Some analogs of the identity F2 n +F2 n+1 = F2 n+1. Fibonacci Quarterly. 1999;305-

Natividad LR. On solving Fibonacci-like sequences of fourth, fth and sixth order. International Journal of Mathematics and Computing. 2013;3(2).

Rathore GPS, Sikhwal O, Choudhary R. Formula for nding nth term of Fibonacci-Like sequence of higher order. International Journal of Mathematics and its Applications. 2016;4(2- D):75-80.

Sloane NJA. The on-line encyclopedia of integer sequences. Available:

Bicknell N. A primer on the Pell sequence and related sequence. Fibonacci Quarterly. 1975;13(4):345-349.

Dasdemir A. On the Pell, Pell-Lucas and modied Pell numbers by Matrix method. Applied Mathematical Sciences. 2011;5(64):3173-3181.

Ercolano J. Matrix generator of Pell sequence. Fibonacci Quarterly. 1979;17(1):71-77.

Gokbas H, Kose H. Some sum formulas for products of Pell and Pell-Lucas numbers. Int. J. Adv. Appl. Math. and Mech. 2017;4(4):1-4.

Horadam AF. Pell Identities. Fibonacci Quarterly. 1971;9(3):245-263.

Kilic E. Tasci D. The linear algebra of the Pell Matrix. Boletn de la Sociedad Matematica Mexicana. 2005;3(11).

Koshy T. Pell and Pell-Lucas numbers with applications. Springer, New York; 2014.

Melham R. Sums involving bonacci and pell numbers. Portugaliae Mathematica. 1999;56(3): 309-317.

Yagmur T. New approach to Pell and Pell-Lucas sequences. Kyungpook Math. J. 2019;59:23-34.

Kilic E, Tasci D. The generalized Binet formula, representation and sums of the generalized order-k Pell numbers. Taiwanese Journal of Mathematics. 2006;10(6):1661-1670.

Kilic E, Stanica P. A matrix approach for general higher order linear Recurrences. Bulletin of the Malaysian Mathematical Sciences Society. 2011;34(1) :51{67.

Soykan Y. On generalized third-order Pell numbers. Asian Journal of Advanced Research and
Reports. 2019;6(1):1-18.

Soykan Y. A study of generalized fourth-order Pell sequences. Journal of Scientic Research and Reports. 2019;25(1-2):1-18. 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.

Soykan Y. Simson identity of generalized m-step bonacci numbers; 2019. arXiv:1903.01313v1[math.NT].

Kalman D. generalized bonacci numbers by matrix methods. Fibonacci Quarterly. 1982;20(1):73-76.