Extensions to the Zeckendorf Triangle

A. G. Shannon and J. V. Leyendekkers
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 5, Pages 31—34
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Authors and affiliations

A. G. Shannon
Faculty of Engineering & IT, University of Technology
Sydney, NSW 2007, Australia

J. V. Leyendekkers
Faculty of Science, The University of Sydney
NSW 2006, Australia

Abstract

This note extends some of the characteristics of a Zeckendorf triangle composed of Fibonacci number multiples of the Fibonacci sequence.

Keywords

  • Fibonacci numbers
  • Convolutions
  • Recurrence relations
  • Kronecker delta
  • Zeckendorf representations
  • Riordan group

AMS Classification

  • 11B39
  • 03G10

References

  1. Cook, C. K., A. G. Shannon. Generalized Fibonacci and Lucas Sequences with Pascal-type Arrays. Notes on Number Theory and Discrete Mathematics . Vol. 12, 2006, No. 4, 1–9.
  2. Griffiths, M. Digit Proportions in Zeckendorf Representations. The Fibonacci Quarterly . Vol. 48, 2010, No. 2, 168–174.
  3. Hilton, P., J. Pedersen. Mathematics, Models, and Magz. Part 1: Patterns in Pascal’s Triangle and Tetrahedron. Mathematics Magazine. Vol. 85, 2012, No. 2, 79–109.
  4. Hoggatt, V. E. Jr. A New Angle on Pascal’s Triangle. The Fibonacci Quarterly. Vol. 6, 1968, No. 4, 221–234.
  5. Hoggatt, V. E. Jr., M. Bicknell-Johnson. Fibonacci Convolution Sequences. The Fibonacci Quarterly. Vol. 15, 1977, No. 2, 117–122.
  6. Shannon, A. G. A Note on Some Diagonal, Row and Partial Column Sums of a Zeckendorf Triangle. Notes on Number Theory and Discrete Mathematics. Vol. 16, 2010, No. 2, 33–36.
  7. Shapiro, L. W., S. Getu, W.-J. Wo an, L. C. Woodson. The Riordan Group. Discrete Applied Mathematics. Vol. 34, 1991, 229–239.

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Cite this paper

APA

Shannon, A. , & Leyendekkers, J. (2014). Extensions to the Zeckendorf Triangle . Notes on Number Theory and Discrete Mathematics, 20(5), 31-34.

Chicago

Shannon, AG, and JV Leyendekkers. “Extensions to the Zeckendorf Triangle .” Notes on Number Theory and Discrete Mathematics 20, no. 5 (2014): 31-34.

MLA

Shannon, AG, and JV Leyendekkers. “Extensions to the Zeckendorf Triangle.” Notes on Number Theory and Discrete Mathematics 20.5 (2014): 31-34. Print.

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