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.
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.
Keywords
(s;t)-Pell sequence Gaussian Pell sequence (s;t)-Gaussian Pell sequence (s;t)-Gaussian Pell matrix sequence
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.
Details
| Primary Language | English |
|---|---|
| Journal Section | Araştırma Makalesi |
| Authors | |
| Publication Date | March 12, 2019 |
| Submission Date | October 13, 2018 |
| Acceptance Date | February 5, 2019 |
| Published in Issue | Year 2019 Volume: 8 Issue: 1 |
