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On the order-m generalized Fibonacci k-numbers

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  • Akbulak, Mehmet
  • Bozkurt, Durmuş

Abstract

In this paper, we defined order-m generalized Fibonacci k -numbers by matrix representation. Using this matrix representation we obtained sums, some identities and the generalized Binet formula of generalized order-m Fibonacci k-numbers.

Suggested Citation

  • Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1347-1355
    DOI: 10.1016/j.chaos.2009.03.019
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    1. Marek-Crnjac, L., 2006. "Different Higgs models and the number of Higgs particles," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 575-579.
    2. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.
    3. Filho, R.N.Costa & Albuquerque, E.L., 1999. "Fractal aspects of the spin wave spectra in pure and generalized Fibonacci anisotropic magnetic superlattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(3), pages 545-554.
    4. Marek-Crnjac, L., 2006. "The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1113-1118.
    5. Kilic, E. & Stakhov, A.P., 2009. "On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2210-2221.
    6. El Naschie, M.S., 2009. "E-eight exceptional Lie groups, Fibonacci lattices and the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1340-1343.
    7. El Naschie, M.S., 2007. "Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 911-915.
    8. Mauriz, P.W. & Vasconcelos, M.S. & Albuquerque, E.L., 2003. "Specific heat properties of electrons in generalized Fibonacci quasicrystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 101-113.
    9. P. D. Sesion & E. L. Albuquerque & C. Chesman & V. N. Freire, 2007. "Acoustic phonon transmission spectra in piezoelectric AlN/GaN Fibonacci phononic crystals," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(4), pages 379-387, August.
    10. Ma, Zheng-Yi & Hu, Ya-Hong & Lan, Jia-Cheng, 2008. "Application of Fibonacci tane function to nonlinear differential-difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 303-308.
    11. El Naschie, M.S., 2007. "Estimating the experimental value of the electromagnetic fine structure constant α¯0=1/137.036 using the Leech lattice in conjunction with the monster group and Spher’s kissing number in 24 dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 383-387.
    12. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
    13. Chen, Tai-Liang & Cheng, Ching-Hsue & Jong Teoh, Hia, 2007. "Fuzzy time-series based on Fibonacci sequence for stock price forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 377-390.
    14. Falcón, Sergio & Plaza, Ángel, 2008. "The k-Fibonacci hyperbolic functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 409-420.
    15. El Naschie, M.S., 2007. "On the topological ground state of E-infinity spacetime and the super string connection," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 468-470.
    16. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
    17. Albuquerque, E.L & Guimarães, E.S, 2000. "Magnetic polaritons in Fibonacci quasicrystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(3), pages 405-414.
    18. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    19. Naschie, M.S.El, 2005. "Deriving the essential features of the standard model from the general theory of relativity," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 941-946.
    20. Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
    21. El Naschie, M.S., 2007. "From symmetry to particles," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 427-430.
    22. El Naschie, M.S., 2005. "Stability Analysis of the two-slit experiment with quantum particles," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 291-294.
    23. El Naschie, M.S., 2007. "Hilbert space, Poincaré dodecahedron and golden mean transfiniteness," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 787-793.
    24. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    25. El Naschie, M.S., 2005. "Experimental and theoretical arguments for the number and the mass of the Higgs particles," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1091-1098.
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    2. Florek, Wojciech, 2018. "A class of generalized Tribonacci sequences applied to counting problems," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 809-821.

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