A. G. Shannon

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

Volume 16, 2010, Number 2, Pages 33–36

**Full paper (PDF, 114 Kb)**

## Details

### Authors and affiliations

A. G. Shannon

*Warrane College, The University of New South Wales,
Kensington, NSW 1465, Australia*

### Abstract

This note fleshes out some of the characteristics of what is referred to as a Zeckendorf triangle which is composed of Fibonacci number multiples of the Fibonacci sequence. It arose it arose in an infinite binary matrix related to the Zeckendorf representations of the non-negative integers.

### Keywords

- Fibonacci numbers
- Convolutions
- Recurrence relations
- Kronecker delta
- Zeckendorf representations

### AMS Classification

- 11B39
- 03G10

### References

- Bondarenko, Boris A. 1993. Generalized Pascal Triangles and Pyramids: Their Fractals, Graphs and Pyramids. (Translated by Richard C. Bollinger.) Santa Clara, CA: The Fibonacci Association.
- Cook, Charles K., A.G. Shannon. 2006. Generalized Fibonacci and Lucas Sequences with Pascal-type Arrays. Notes on Number Theory & Discrete Mathematics. 12 (4): 1-9.
- Griffiths, Martin. 2010. Digit Proportions in Zeckendorf Representations. The Fibonacci Quarterly. 48 (2): 168-174.
- Hoggatt, V.E. Jr, Marjorie Bicknell-Johnson. 1977. Fibonacci Convolution Sequences. The Fibonacci Quarterly. 15 (2): 117-122.
- Leyendekkers, J.V., A G Shannon. 2001. Expansion of Integer Powers from Fibonacci’s Odd Number Triangle. Notes on Number Theory & Discrete Mathematics, 7 (2): 48-59.
- Ollerton, R.L., A.G. Shannon. 1998. Some Properties of Generalized Pascal squares and Triangles. The Fibonacci Quarterly, 36 (2): 98-109.
- Riordan, J. 1962. Generating Functions for Powers of Fibonacci Numbers. Duke

Mathematical Journal. 29 (1): 5-12. - Shannon, A.G., A.F. Horadam. 2002. Reflections on the Lambda Triangle, The Fibonacci Quarterly, 40 (5): 405 – 416. 27.
- Shannon A. G., J.C. Turner, K.T. Atanassov.1991. A Generalised Tableau Associated with Colored Convolution Trees. Discrete Mathematics. 92: 329-340.
- Sloane, N.J.A., Simon Plouffe. 1995. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press.
- Whittington, S.G., G.M. Torrie, A.J. Guttmann. 1979. The Ising Model with a Free Surface: a Series Analysis Study. Journal of Physics A: Mathematical & General.12 (12): 2449-2456.

## Related papers

## Cite this paper

Shannon, A. G. (2010). A note on some diagonal, row and partial column sums of a Zeckendorf triangle. *Notes on Number Theory and Discrete Mathematics*, 16(2), 33-36.