Research Article
BibTex RIS Cite

(s,t)-Modified Pell Sequence and Its Matrix Representation

Year 2019, Volume: 12 Issue: 2, 863 - 873, 31.08.2019
https://doi.org/10.18185/erzifbed.494358

Abstract

In this paper, we investigate
a generalization of modified Pell sequence, which is called (s,t)
-modified Pell sequence. By
considering this sequence, we define the matrix sequence whose elements are (s,t)
-modified Pell numbers.
Furthermore, we obtain Binet formulas, the generating functions and some sums
formulas of these sequence. Finally, we give some relationships between (s,t)
-Pell and (s,t)-modified Pell matrix
sequences.

References

  • Benjamin, A.T., Plott, S.S., Sellers, J.A. 2008. “Tiling proofs of recent sum identities involving Pell numbers”, Annals of Combinatorics, 12, 271-278.
  • Bicnell, M. 1975. “A primer on the Pell sequence and related sequences”, The Fib. Quart., 13(4), 345-349.
  • Civciv, H., Türkmen, R. 2008a. “On the (s,t)-Fibonacci and Fibonacci matrix sequence”, Ars Combinatoria, 87, 161-173.
  • Civciv, H., Türkmen, R. 2008b. “Notes on the (s,t)-Lucas and Lucas matrix sequences”, Ars Combinatoria, 89, 271-285.
  • Guleç, H.H., Taskara, N. 2012. “On the (s,t)-Pell and (s,t)-Pell-Lucas sequences and their matrix representations”, Applied Mathematics Letters, 25(10), 1554-1559.
  • Horadam, A.F., Filipponi, P. 1995. “Pell and Pell-Lucas numbers with real subscripts”, The Fib. Quart., 33(5), 398-406.
  • Koshy, T. 2001. “Fibonacci and Lucas numbers with applications”, John Wiley and Sons Inc., NY.
  • Stakhoy, A., Rozin, B. 2006. “Theory of Binet formulas for Fibonacci and Lucas p-numbers”, Solition & Fractals, 27(5), 1162-1177.

(s,t)-Modified Pell Dizisi ve Matris Gösterimi

Year 2019, Volume: 12 Issue: 2, 863 - 873, 31.08.2019
https://doi.org/10.18185/erzifbed.494358

Abstract

Bu çalışmada, (s,t)-modified Pell dizisi olarak
adlandırılan modified Pell dizisinin bir genellemesini araştırdık. Bu diziyi
dikkate alarak elemanları (s,t)
-modified Pell sayıları olan
matris dizisini tanımladık. Ayrıca, bu dizilerin üreteç fonksiyonlarını, Binet
formüllerini ve bazı toplam formüllerini elde ettik. Son olarak, (s,t)
-Pell ve (s,t)-modified Pell matris dizileri
arasında bazı ilişkiler verdik.

References

  • Benjamin, A.T., Plott, S.S., Sellers, J.A. 2008. “Tiling proofs of recent sum identities involving Pell numbers”, Annals of Combinatorics, 12, 271-278.
  • Bicnell, M. 1975. “A primer on the Pell sequence and related sequences”, The Fib. Quart., 13(4), 345-349.
  • Civciv, H., Türkmen, R. 2008a. “On the (s,t)-Fibonacci and Fibonacci matrix sequence”, Ars Combinatoria, 87, 161-173.
  • Civciv, H., Türkmen, R. 2008b. “Notes on the (s,t)-Lucas and Lucas matrix sequences”, Ars Combinatoria, 89, 271-285.
  • Guleç, H.H., Taskara, N. 2012. “On the (s,t)-Pell and (s,t)-Pell-Lucas sequences and their matrix representations”, Applied Mathematics Letters, 25(10), 1554-1559.
  • Horadam, A.F., Filipponi, P. 1995. “Pell and Pell-Lucas numbers with real subscripts”, The Fib. Quart., 33(5), 398-406.
  • Koshy, T. 2001. “Fibonacci and Lucas numbers with applications”, John Wiley and Sons Inc., NY.
  • Stakhoy, A., Rozin, B. 2006. “Theory of Binet formulas for Fibonacci and Lucas p-numbers”, Solition & Fractals, 27(5), 1162-1177.
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Nusret Karaaslan

Tülay Yağmur

Publication Date August 31, 2019
Published in Issue Year 2019 Volume: 12 Issue: 2

Cite

APA Karaaslan, N., & Yağmur, T. (2019). (s,t)-Modified Pell Sequence and Its Matrix Representation. Erzincan University Journal of Science and Technology, 12(2), 863-873. https://doi.org/10.18185/erzifbed.494358