J. V. Leyendekkers and A. G. Shannon

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

Volume 17, 2011, Number 4, Pages 9—13

**Download full paper: PDF, 34 Kb**

## Details

### Authors and affiliations

A. G. Shannon

*Faculty of Engineering & IT, University of Technology
Sydney, NSW 2007, Australia
*

### Abstract

This note compares and contrasts some properties of binary sequences with matrices and associated recurrence relations in order to stimulate some enrichment exercises and pattern puzzles.

### Keywords

- Binary
- Matrix
- Sequence
- Recurrence relation
- Kronecker delta
- Repunit,
- Fibonacci numbers
- Lucas numbers
- Pell numbers
- Pascal’s triangle

### AMS Classification

- 11A41
- 11A55
- 11A07

### References

- Atanassov, K., V. Atanassova, A. Shannon, J. Turner.
*New Visual Perspectives on Fibonacci Numbers.*New Jersey: World Scientific, 2002. - Austin, R., R. Guy. Binary Sequences without Isolated Ones.
*The Fibonacci Quarterly*. Vol. 16, 1978, 84–87, 96. - Beiler, A. H.
*Recreations in the Theory of Numbers: The Queen of Mathematics Entertains.*New York: Dover, 1966. - Gardner, M.
*Knotted Doughnuts and Other Mathematical Entertainment.*New York: Freeman, 1986. - Iverson, K. E. Notation as a Tool of Thought.
*Communications of the Association for Computing Machinery.*Vol. 23, 1980, 444–465. - Kimberley, C. Polynomials Defined by a Second Order Recurrence, Interlacing Zeros, and Gray Codes.
*The Fibonacci Quarterly*. Vol. 48, 2010, 209–218. - Shannon, A. G. Shrewd Guessing in Problem-solving.
*International Journal of Mathematical Education in Science and Technology.*Vol. 22, 1991, 144–147. - Sloane, N.J.A., S. Plouffe.
*The Encyclopedia of Integer Sequences.*San Diego: Academic Press, 1995. - Sburlati, G. Generalized Fibonacci Sequences and Linear Congruences.
*The Fibonacci Quarterly.*Vol. 40, 2002, 446–452.

## Related papers

## Cite this paper

APAShannon, A. G. (2011). Some recurrence relations for binary sequence matrices, Notes on Number Theory and Discrete Mathematics, 17(4), 9-13.

ChicagoShannon, A. G. “Some Recurrence Relations for Binary Sequence Matrices.” Notes on Number Theory and Discrete Mathematics 17, no. 4 (2011): 9-13.

MLAShannon, A. G. “Some Recurrence Relations for Binary Sequence Matrices.” Notes on Number Theory and Discrete Mathematics 17.4 (2011): 9-13. Print.