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
Full paper (PDF, 133 Kb)

Details

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.