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.
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | August 31, 2019 |
| Published in Issue | Year 2019 Volume: 12 Issue: 2 |