Three-dimensional extensions of Fibonacci sequences. Part 1

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 14, 2008, Number 3, Pages 15–18
Full paper (PDF, 111 Kb)

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Krassimir T. Atanassov

Introduction

The Fibonacci sequence is an object of a lot of generalizations. During the last 25 years the author took part in introduction of some of them, like 2-Fibonacci sequences (together with D. Sasselov and my wife L. Atanassova), sets of Fibonacci sequences (together with A. Shannon and my daughter V. Atanassova), Fibonacci place, Fibonacci space (together with A. Shannon) and others.

In all cases the new sequences are planar objects. Even each of the sequences in the Fibonacci space has a line-form, i.e., planar form.

Now, in a series of papers, we shall introduce the first three-dimensional Fibonacci-like objects. In the present (first) part we shall construct the first two sequences with three-dimensional form that can be project in a plane.

References

1. Atanassova V., A. Shannon, K. Atanassov, Sets of extensions of the Fibonacci sequences. Comptes Rendus de l’Academie bulgare des Sciences, Tome 56, 2003, No. 9, 9-12.