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Gauss (𝒔, 𝒕)-Pell ve Pell-Lucas Dizileri ve Matris Gösterimleri

Year 2019, Volume: 8 Issue: 1, 46 - 59, 12.03.2019
https://doi.org/10.17798/bitlisfen.470181

Abstract

Bu
çalışmada,
Gauss (s,t)-Pell
ve Gauss
(s,t)-Pell-Lucas
dizilerini tanımladık. Sonra, bu dizileri kullanarak Gauss (s,t)
-Pell
ve Gauss (s,t)
-Pell-Lucas
matris dizilerini tanımladık. Daha sonra, bu dizilerin üreteç fonksiyonlarını,
Binet formüllerini ve bazı toplam formüllerini verdik. Son olarak,
Gauss (s,t)-Pell ve Gauss (s,t)-Pell-Lucas matris dizileri arasında bazı ilişkileri elde
ettik.

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.
  • Berzsenyi G. 1977. Gaussian Fibonacci Numbers. Fibonacci Quarterly 15(3): 233-236.
  • Civciv H., Türkmen R. 2008. Notes on the (s,t)-Lucas and Lucas Matrix Sequences, Ars Combinatoria 89, 271–285.
  • Civciv H., Türkmen R. 2008. On the (s,t)-Fibonacci and Fibonacci Matrix Sequences, Ars Combinatoria 87, 161–173.
  • Good J.J. 1981. Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio, Fibonacci Quaterly 31 (1): 7-20.
  • Gulec 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.
  • Halıcı S., Öz S. 2016. On Some Gaussian Pell and Pell-Lucas Numbers, Ordu Univ. Science and Technology Journal 6(1): 8-18.
  • Harman C.J. 1981. Complex Fibonacci Numbers, Fibonacci Quaterly 19(1): 82-86.
  • Horadam A.F. 1963. Complex Fibonacci Numbers and Fibonacci Quaternions, American Math. Monthly 70, 289-291.
  • Jordan J.H. 1965. Gaussian Fibonacci and Lucas Numbers, Fibonacci Quarterly 3, 315-318.
  • Koshy T. 2001. Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc., NY.
  • Pektaş P. 2015. (s,t)-Gauss Fibonacci ve Lucas Sayılarının Kombinatorial Özellikleri Üzerine. Pamukkale Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek lisans tezi, 53s, Denizli.
  • Pethe S., Horadam A.F. 1986. Generalized Gaussian Fibonacci Numbers, Bull. Austral. Math. Soc. 33(1): 37-48.
  • Stakhov A., Rozin B. 2006. Theory of Binet Formulas for Fibonacci and Lucas p-numbers, Solitions & Fractals 27(5): 1162-1177.
  • Taskara N., Uslu K., Guleç H.H. 2010. On the Properties of Lucas Numbers With Binomial Coefficients, Applied Mathematics Letters 23(1): 68-72.
  • Yagmur T., Karaaslan N. 2018. Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence, Aksaray J. Sci. Eng. 2(1): 63-72.

Gaussian (𝒔, 𝒕)-Pell and Pell-Lucas Sequences and Their Matrix Representations

Year 2019, Volume: 8 Issue: 1, 46 - 59, 12.03.2019
https://doi.org/10.17798/bitlisfen.470181

Abstract

In this study, we define the Gaussian (s,t)-Pell and Gaussian (s,t)-Pell-Lucas sequences. Then, by using
these sequences we define Gaussian (s,t)-Pell and Gaussian (s,t)-Pell-Lucas matrix sequences. Thereafter,
we give generating functions, Binet’s formulas and some summation formulas of
these sequences. Finally, we obtain some 
relationships between Gaussian (s,t)-Pell and Gaussian (s,t)-Pell-Lucas 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.
  • Berzsenyi G. 1977. Gaussian Fibonacci Numbers. Fibonacci Quarterly 15(3): 233-236.
  • Civciv H., Türkmen R. 2008. Notes on the (s,t)-Lucas and Lucas Matrix Sequences, Ars Combinatoria 89, 271–285.
  • Civciv H., Türkmen R. 2008. On the (s,t)-Fibonacci and Fibonacci Matrix Sequences, Ars Combinatoria 87, 161–173.
  • Good J.J. 1981. Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio, Fibonacci Quaterly 31 (1): 7-20.
  • Gulec 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.
  • Halıcı S., Öz S. 2016. On Some Gaussian Pell and Pell-Lucas Numbers, Ordu Univ. Science and Technology Journal 6(1): 8-18.
  • Harman C.J. 1981. Complex Fibonacci Numbers, Fibonacci Quaterly 19(1): 82-86.
  • Horadam A.F. 1963. Complex Fibonacci Numbers and Fibonacci Quaternions, American Math. Monthly 70, 289-291.
  • Jordan J.H. 1965. Gaussian Fibonacci and Lucas Numbers, Fibonacci Quarterly 3, 315-318.
  • Koshy T. 2001. Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc., NY.
  • Pektaş P. 2015. (s,t)-Gauss Fibonacci ve Lucas Sayılarının Kombinatorial Özellikleri Üzerine. Pamukkale Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek lisans tezi, 53s, Denizli.
  • Pethe S., Horadam A.F. 1986. Generalized Gaussian Fibonacci Numbers, Bull. Austral. Math. Soc. 33(1): 37-48.
  • Stakhov A., Rozin B. 2006. Theory of Binet Formulas for Fibonacci and Lucas p-numbers, Solitions & Fractals 27(5): 1162-1177.
  • Taskara N., Uslu K., Guleç H.H. 2010. On the Properties of Lucas Numbers With Binomial Coefficients, Applied Mathematics Letters 23(1): 68-72.
  • Yagmur T., Karaaslan N. 2018. Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence, Aksaray J. Sci. Eng. 2(1): 63-72.
There are 16 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Nusret Karaaslan

Tülay Yağmur

Publication Date March 12, 2019
Submission Date October 13, 2018
Acceptance Date February 5, 2019
Published in Issue Year 2019 Volume: 8 Issue: 1

Cite

IEEE N. Karaaslan and T. Yağmur, “Gaussian (𝒔, 𝒕)-Pell and Pell-Lucas Sequences and Their Matrix Representations”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 8, no. 1, pp. 46–59, 2019, doi: 10.17798/bitlisfen.470181.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS