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

Öz

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.

Anahtar Kelimeler

• Modified Pell sequence,(s;t)-modified Pell sequence,(s;t)-modified Pell matrix sequence

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

Öz

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.

Anahtar Kelimeler

• Modified Pell dizisi,(s;t)-modified Pell dizisi,(s;t)-modified Pell matris dizisi

Kaynakça

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2. Bicnell, M. 1975. “A primer on the Pell sequence and related sequences”, The Fib. Quart., 13(4), 345-349.
3. Civciv, H., Türkmen, R. 2008a. “On the (s,t)-Fibonacci and Fibonacci matrix sequence”, Ars Combinatoria, 87, 161-173.
4. Civciv, H., Türkmen, R. 2008b. “Notes on the (s,t)-Lucas and Lucas matrix sequences”, Ars Combinatoria, 89, 271-285.
5. 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.
6. Horadam, A.F., Filipponi, P. 1995. “Pell and Pell-Lucas numbers with real subscripts”, The Fib. Quart., 33(5), 398-406.
7. Koshy, T. 2001. “Fibonacci and Lucas numbers with applications”, John Wiley and Sons Inc., NY.
8. Stakhoy, A., Rozin, B. 2006. “Theory of Binet formulas for Fibonacci and Lucas p-numbers”, Solition & Fractals, 27(5), 1162-1177.