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.
- J. Ercolano, Matrix generators of Pell sequences, Fibonacci Quart., 17 (1) (1979), 71-77.
- M. Edson, S. Lewis and O. Yayenie, The k-periodic Fibonacci sequence and extended Binet's formula, Integer 11 (2011), 1-12. https://doi.org/10.1515/integ.2011.001
- M. Edson and O. Yayenie, A new generalization of Fibonacci sequence and extended Binet's formula, Integer 9 (2009), 639-654.
- Y. K. Gupta, Y. K. Panwar and O. Sikhwal, Generalized Fibonacci Sequences, Theoretical Mathematics and Applications 2 (2) (2012), 115-124.
- 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. https://doi.org/10.12691/tjant-2-6-9
- A. F. Horadam, A generalized Fibonacci sequences, Amer. Math. Monthly 68 (1961), 455-459. https://doi.org/10.2307/2311099
-
E. Kilic, Sums of the squares of terms of sequence {
$u_n$ }, Proc. Indian Acad. Sci.(Math. Sci.) 118 (1), February 2008, 27-41. https://doi.org/10.1007/s12044-008-0003-y - D. Kalman and R. Mena, The Fibonacci numbers - Exposed, The Mathematical Magazine 2 (2002).
- J. R. Silvester, Fibonacci properties by matrix methods, Mathematical Gazette 63 (1979), 188-191. https://doi.org/10.2307/3617892
-
K. S. Williams, The nth power of a
$2{\times}2$ matrix, Math. Mag. 65 (5) (1992), 336. https://doi.org/10.2307/2691246 - O. Yayenie, A note on generalized Fibonacci sequences, Applied Mathematics and Computation 217 (2011), 5603-5611. https://doi.org/10.1016/j.amc.2010.12.038
- H. Zhang and Z. Wu, On the reciprocal sums of the generalized Fibonacci sequences, Adv. Differ. Equ. (2013), Article ID 377 (2013).
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