Some Matrix Applications on the Special Integer Number Sequences

Year 2023, , 209 - 216, 31.05.2023

Ümmügülsün Akbaba

https://doi.org/10.35193/bseufbd.1219370

Abstract

In this paper, the matrices related to Fibonacci, Lucas, Pell, and Pell-Lucas numbers have been examined. By using these matrices new identities related to these integer sequences have been investigated.

Keywords

Matrix Method, Fibonacci Numbers, Pell Numbers, Lucas Numbers, Pell-Lucas Numbers

Özel Tam Sayı Dizilerinin Bazı Matris Uygulamaları

Abstract

Bu çalışmada, Fibonacci, Lucas, Pell ve Pell-Lucas sayı dizileri ile ilgili matrisler incelendi. Bu matrisleri kullanarak bu tam sayı dizileri ile ilgili yeni özdeşlikler araştırıldı.

Keywords

Matris Metodu, Fibonacci Sayıları, Pell Sayıları, Lucas Sayıları, Pell-Lucas Sayıları

References

• Silvester, J.R. (1979). Fibonacci properties by matrix methods. The Mathematical Gazette, 63(425), 188-191.
• Ercolano, J. (1979). Matrix generator of Pell sequence. Fibonacci Quarterly, 17(1), 71-77.
• Hoggatt, V.E. (1969). Fibonacci and Lucas Numbers. Palo Alto: CA: Houghton- Mifflin.
• Köken, F., & Bozkurt D. (2010). On Lucas numbers by the matrix method. Hacettepe Journal of Mathematics and Statistics, 39, 471-475.
• Akbaba, Ü., Değer, A.H., & Tuylu, T. (2018). On some connections between suborbital graphs and special sequences. Turkish Journal of Mathematics and Computer Science, 10,134-143.
• Değer, A.H. (2017).Vertices of paths of minimal lengths on suborbital graphs. Filomat, 31,913-923.
• Değer, A.H. (2017). Relationships with the Fibonacci numbers and the special vertices of the suborbital graphs. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 7, 168-180.
• Akbaba, Ü. & Değer A.H. (2022). Relation between matrices and the suborbital graphs by the special number sequences. Turkish Journal of Mathematics, 46 (3), 753-767.
• Bicknell, M., & Hoggatt, V.E. (1963). Fibonacci Matrices and Lambda Functions. Fibonacci Quarterly, 1(2) 47-52.
• Koshy, T. (2001). Fibonacci and Lucas numbers with applications, A Wiley- Interscience Publication, Canada.
• Koshy, T. (2014). Pell and Pell-Lucas Numbers with Applications. New York: Springer.