On two new two-dimensional extensions of the Fibonacci sequence

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 3, Pages 115—122
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Authors and affiliations

Krassimir T. Atanassov
Department of Bioinformatics and Mathematical Modelling
IBPhBME, Bulgarian Academy of Sciences
Acad. G. Bonchev Str. Bl. 105, Sofia-1113, Bulgaria
and
Intelligent Systems Laboratory
Prof. Asen Zlatarov University, Bourgas-8000, Bulgaria

Abstract

Two new two-dimensional extensions of the Fibonacci sequence are introduced. Explicit formulas for their n-th members are given.

Keywords

  • Fibonacci sequence

AMS Classification

  • 11B39

References

  1. Atanassov, K., Atanassova, L., & Sasselov, D. (1985) A new perspective to the generalization of the Fibonacci sequence, The Fibonacci Quarterly, 23 (1), 21–28.
  2. Atanassov, K. (1986) On a second new generalization of the Fibonacci sequence. The Fibonacci Quarterly, 24(4), 362–365.
  3. Atanassov, K., Atanassova, V., Shannon, A., & Turner, J. (2002) New Visual Perspectives on Fibonacci Numbers. World Scientific, New Jersey.
  4. Lee, J.-Z., & Lee, J.-S. (1987) Some properties of the generalization of the Fibonacci sequence. The Fibonacci Quarterly, 25(2), 111–117.

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Cite this paper

APA

Atanassov, K. T. (2017). On two new two-dimensional extensions of the Fibonacci sequence Notes on Number Theory and Discrete Mathematics, 23(3), 115-122.

Chicago

Atanassov, Krassimir T. “On two new two-dimensional extensions of the Fibonacci sequence.” Notes on Number Theory and Discrete Mathematics 23, no. 3 (2017): 115-122.

MLA

Atanassov, Krassimir T. “On two new two-dimensional extensions of the Fibonacci sequence.” Notes on Number Theory and Discrete Mathematics 23.3 (2017): 115-122. Print.

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