J. C. Turner

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 4, 1998, Number 4, Pages 135–147

**Full paper (PDF, 8187 Kb)**

## Details

### Authors and affiliations

J. C. Turner

*University of Waikato,
Hamilton, New Zealand*

### Abstract

A particular form of generalized Fibonacci sequence is defined, and supplied with the generic name *track*. Reasons for doing this are discussed, and simple examples of *tracks* are given. Then an example which occurs in Fibonacci Vector Geometry, namely the vector-product track, is treated in some detail.

### Keywords

- Generalized Fibonacci sequence
- Fibonacci vector sequence
- Vector-product sequence
- Track
- Track pattern
- Fibonacci words
- Fibonacci vector geometry

### AMS Classification

- 11B37
- 11B39
- 10A35

### References

- Wai-Fong Chuan. “Embedding Fibonacci Words into Fibonacci Word Patterns.” In G. Bergum et al. (eds.), Applications of Fibonacci Numbers. 5 Kluwer A. P. 1993: pp 113-127.
- Wai-Fong Chuan. “Subwords of the Golden Sequence and Fibonacci Words.” In G. Bergum et al. (eds.), Applications of Fibonacci Numbers. 6 Kluwer A. P. 1996: pp 73-84.
- J. C. Turner. “Fibonacci Word Patterns and Binary Sequences.” The Fibonacci Quarterly, 26, No. 3, 1988: pp 233-246.
- J. C. Turner and A. G. Schaake. “On a Model of the Modular Group.” In G. E. Bergum et al. (eds.), Applications of Fibonacci Numbers 6 Kluwer A. P. (1996).
- J. C. Turner and A. G. Shannon. “Introduction to a Fibonacci Vector Geometry.” In G. E. Bergum et al. (eds.), Applications of Fibonacci Numbers 7 Kluwer A. P. (1998).
- J. C. Turner. “On Vector Sequence Recurrence Equations in Fibonacci Vector Geometry.” In F. Howard et al. (eds.), Applications of Fibonacci Numbers. 8 Kluwer A. P. (1999).
- J. C. Turner and A.G. Shannon. “On Fibonacci Sequences, Geometry and
*m*-Square Equations.” (to appear, The Fibonacci Quarterly, 1999.)

## Related papers

## Cite this paper

Turner, J. C. (1998). The Fibonacci track form, with applications in Fibonacci vector geometry. *Notes on Number Theory and Discrete Mathematics*, 4(4), 135-147.