References
- M. Adam and N. Assimakis, k-step sum and m-step gap Fibonacci sequence, ISRN Discrete Mathematics, v. 2014, Article ID 374902, (2014), 7 pages, http://doi.org/10.1155/2014/374902.
- M. Adam, N. Assimakis and G. Tziallas, Generalized k, m-step Fibonacci sequences and matrices, Proceedings of the 12th AHA conference, (2014).
- N. Assimakis, M. Adam and C. Triantafillou, Lainiotis filter, golden section and Fibonacci sequence, Signal Processing, 93(4), (2013), 721–730. doi: 10.1016/j.sigpro.2012.09.014
- M. Elia, Derived Sequences, The Tribonacci Recurrence and Cubic Forms, The Fibonacci Quarterly, 39(2), (2001), 107–115.
- M.C. Er, The matrices of Fibonacci numbers, The Fibonacci Quarterly, 22(2), (May, 1984), 134–139.
- M.C. Er, Sums of Fibonacci numbers by matrix methods, The Fibonacci Quarterly, 22(3), (1984), 204–207.
- Xudan Fu and Xia Zhou, On matrices related with Fibonacci and Lucas numbers, Applied Mathematics and Computation, 200, (2008), 96–100.
- Lixing Han, Michael Neumann and Jianhong Xu, On the roots of certain polynomials arising from the analysis of the NelderMead simplex method, Linear Algebra and its Applications, 363, (2003), 109–124. doi: 10.1016/S0024-3795(02)00485-8
- R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 2005.
- John Ivie, A general Q-matrix, The Fibonacci Quarterly, 10(3), (1972), 255–264.
- Erdal Karaduman, An application of Fibonacci numbers in matrices, Applied Mathematics and Computation, 147, (2004), 903–908. doi: 10.1016/S0096-3003(02)00827-5
- Dan Kalman, Generalized Fibonacci numbers by matrix methods, The Fibonacci Quarterly, 20(1), (1982), 73–76.
- T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, Inc., New York, 2001.
- G.-Y. Lee, S.-G. Lee and H.-G. Shin, On the k-Generalized Fibonacci matrix Q, Linear Algebra and its Applications, 251, (1997), 73–88. doi: 10.1016/0024-3795(95)00553-6
- M. Mishra, P. Mishra, M.C. Adhikary and S. Kumar, Image encryption using Fibonacci-Lucas transformation, International Journal on Cryptography and Information Security (IJCIS), 2(3), (September, 2012), 131–141. doi: 10.5121/ijcis.2012.2312
- D. Noutsos, Perron-Frobenius theory and some extensions, Como, Italy, May 2008, the presentation available at http://www.math.uoi.gr/dnoutsos/Papers-pdf-files/slide-perron.pdf.
- A.S. Posamentier and I. Lehmann, The Fabulous Fibonacci Numbers, Prometheus Books , New York, 2007.
- L.-P. Shao, Z. Qin, H.-L. Gao and X.-C. Heng, 2D triangular mappings and their applications in scrambling rectangle image, Information Technology Journal, 7(1), (2008), 40–47. doi: 10.3923/itj.2008.40.47
- B. Sharpe, On Sums F2x ± F2y, The Fibonacci Quarterly, 3(1), (Feb. 1965), 63.
- N.J.A. Sloane, editor (2003), The On-Line Encyclopedia of Integer Sequences, available at http://oeis.org/.
- Predrag Stanimirović, Jovana Nikolov and Ivan Stanimirović, A generalization of Fibonacci and Lucas matrices, Discrete Applied Mathematics, 156, (2008), 2606–2619. doi: 10.1016/j.dam.2007.09.028
- Bo Tan and Zhi-Ying Wen, Some properties of the Tribonacci sequence, European Journal of Combinatorics, 28, (2007), 1703–1719.
- S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Dover Publications, New York , 2007.