DOI: https://doi.org/10.11568/kjm.2016.24.4.681

### Some properties of the generalized Fibonacci sequence $\{q_n\}$ by matrix methods

#### Abstract

In this note, we consider a generalized Fibonacci sequence $\{q_n\}$. We give a generating matrix for $\{q_n\}$. With the aid of this matrix, we derive and re-prove some properties involving terms of this sequence

#### Keywords

#### Subject classification

11B37, 11B39, 11B83#### Sponsor(s)

#### Full Text:

PDF#### References

A. Borges, P. Catarino, A. P. Aires, P. Vasco and H. Campos, Two-by-two matrices involving k-Fibonacci and k-Lucas sequences, Applied Mathematical Sciences, 8 (34) (2014), 659–1666. (Google Scholar)

J. Ercolano, Matrix generators of Pell sequences, Fibonacci Quart., 17 (1) (1979), 71–77. (Google Scholar)

M. Edson, S. Lewis and O. Yayenie, The k-periodic Fibonacci sequence and extended Binet’s formula, Integer 11 (2011), 1–12. (Google Scholar)

M. Edson and O. Yayenie, A new generalization of Fibonacci sequence and ex- tended Binet’s formula, Integer 9 (2009), 639–654. (Google Scholar)

Y. K. Gupta, Y. K. Panwar and O. Sikhwal, Generalized Fibonacci Sequences, Theoretical Mathematics and Applications 2 (2) (2012), 115–124. (Google Scholar)

Y. K. Gupta, M. Singh and O. Sikhwal, Generalized Fibonacci-Like Sequence Associated with Fibonacci and Lucas Sequences, Turkish Journal of Analysis and Number Theory 2 (6) (2014), 233–238. (Google Scholar)

A. F. Horadam, A generalized Fibonacci sequences, Amer. Math. Monthly 68 (1961), 455–459. (Google Scholar)

E. Kilic, Sums of the squares of terms of sequence {un}, Proc. Indian Acad. Sci.(Math. Sci.) 118 (1), February 2008, 27–41. (Google Scholar)

D. Kalman and R. Mena, The Fibonacci numbers - Exposed, The Mathematical Magazine 2 (2002). (Google Scholar)

J. R. Silvester, Fibonacci properties by matrix methods, Mathematical Gazette 63 (1979), 188–191. (Google Scholar)

K. S. Williams, The nth power of a 2 × 2 matrix, Math. Mag. 65 (5) (1992), 336. (Google Scholar)

O. Yayenie, A note on generalized Fibonacci sequences, Applied Mathematics and Computation 217 (2011), 5603–5611. (Google Scholar)

H. Zhang and Z. Wu, On the reciprocal sums of the generalized Fibonacci sequences, Adv. Differ. Equ. (2013), Article ID 377 (2013). (Google Scholar)

### Refbacks

- There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr