Advanced search
Publication Cover
Cogent Mathematics Volume 3, 2016 - Issue 1
Submit an article Journal homepage
2,674
Views
0
CrossRef citations to date
0
Altmetric
Research Article

On the complex k-Fibonacci numbers

Sergio FalconDepartment of Mathematics, University of Las Palmas de Gran Canaria, 35017-Las Palmas de Gran Canaria, SpainCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0001-9917-3101View further author information
ORCID Icon |
Benchawan WiwatanapatapheeCurtin University, AustraliaView further author information
(Reviewing Editor)
Article: 1201944 | Received 19 Jan 2015, Accepted 20 May 2016, Published online: 27 Jul 2016

References

  • Bolat, C., & Kse, H. (2010). On the properties of k-Fibonacci numbers. International Journal of Contemporary Mathematical Sciences, 5, 1097–1105.
  • El Naschie, M. S. (2001). Notes on superstrings and the infinite sums of Fibonacci and Lucas numbers. Chaos, Solitons & Fractals, 12, 1937–1940.
  • El Naschie, M. S. (2006). Topics in the mathematical physics of E-infinity theory. Chaos, Solitons & Fractals, 3, 656–663.
  • Falcon, S., & Plaza, A. (2007a). On the Fibonacci k-numbers. Chaos, Solitons & Fractals, 32, 1615–1624.
  • Falcon, S., & Plaza, A. (2007b). The k-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons & Fractals, 33, 38–49.
  • Falcon, S., & Plaza, A. (2009a). k-Fibonacci sequences modulo m. Chaos, Solitons & Fractals, 41, 497–504.
  • Falcon, S., & Plaza, A. (2009b). Binomial transforms of the k-Fibonacci sequence. International Journal of Nonlinear Sciences & Numerical Simulation, 10, 1527–1538.
  • Hoggat, V. E. (1969). Fibonacci and Lucas numbers. Boston, MA: Houghton-Mifflin.
  • Horadam, A. F. (1961). A generalized Fibonacci sequence. Mathematics Magazine, 68, 455–459.
  • Koshy, T. (2001). Fibonacci and Lucas numbers with applications. New York, NY: A Wiley-Interscience.
  • Ram{\’i}rez, J. L. (2015). Some combinatorial properties of the k-Fibonacci and k-Lucas Quaternions. Analele stiintifice ale Universitatii Ovidius Constanta, 23, 201–212.
  • Salas, A. (2011). About k-Fibonaci numbers and their associated numbers. International Mathematical Forum, 50, 2473–2479.
  • Sloane, N. J. A. (2006). The on-line encyclopedia of integer sequences. Retrieved from http://www.research.att.com/njas/sequences/
  • Spinadel, V. W. (2002). The metallic means family and forbidden symmetries. International Journal of Mathematics, 2, 279–288.
  • Vajda, S. (1989). Fibonacci & Lucas numbers, and the golden section. Theory and applications. Mineola, NY: Ellis Horwood.
  • Weisstein, E. W. (2009). Gaussian integer, From MathWorld-A Wolfram Web resource. Retrieved from http://mathworld.wolfram.com/GaussianInteger.html

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.