Some recurrence relations for binary sequence matrices

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
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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

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

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Cite this paper

APA

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

Chicago

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

MLA

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

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