Identities of Generalized Pell and Pell-Lucas Sequences

Yıl 2022, Cilt: 3 Sayı: 2, 46 - 55, 27.12.2022

Yashwant Panwar

https://doi.org/10.46572/naturengs.1171676

Öz

In this paper, we present sums of generalized Pell and Pell-Lucas sequences. These sequences were introduced by Tulay Yagmur in 2019. We establish some connection formulae of involving them. Also, we present its two cross two matrix representation. We have used their Generating function, Binet’s formula and Induction method to derive the identities.

Anahtar Kelimeler

Generalized Pell sequence, Generalized Pell-Lucas sequence, Binet’s formula, Generating function.

Kaynakça

• [1] Bilgici, G. (2014). New Generalizations of Fibonacci and Lucas Sequences, Applied Mathematical Sciences, 8(29): 1429-1437.
• [2] Dasdemir A. (2011). On the Pell, Pell-Lucas and modified Pell numbers by matrix method. Appl. Math. Sci., 5(64): 3173–3181.
• [3] Falcon, S., and Plaza, A. (2007). On the k-Fibonacci Numbers, Chaos,Solitons and Fractals, 32(5): 1615-1624. https://doi.org/10.1016/j.chaos.2006.09.022
• [4] Gulec HH, Taskara N. (2012). On the (s,t)-Pell and (s,t)-Pell-Lucas sequences and their matrix representations. Appl. Math. Lett., 25: 1554–1559.
• [5] Horadam, A.F. (1971). Pell Identities, The Fibonacci Quarterly, 9(3), 245-263.
• [6] Koshy T. Fibonacci and Lucas numbers with applications. New York, Wiley- Interscience, 2001.
• [7] Koshy T. Pell and Pell-Lucas numbers with applications, Springer, Berlin, 2014.
• [8] Taşyurdu Y, Cobanoğlu N, Dilmen Z. (2016). On The a New Family of k-Fibonacci Numbers. Erzincan University Journal of Science and Technology, 9(1): 95-101.
• [9] Yagmur T. (2019). New Approach to Pell and Pell-Lucas Sequence. Kyungpook Mathematical Journal, 59(1): 23-34.