An extremal problem related to the Fibonacci sequence

K. T. Atanassov, R. D. Knott, R. L. Ollerton and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 12, 2006, Number 2, Pages 13—20
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Authors and affiliations

K. T. Atanassov
Centre for Biomedical Engineering, Bulgarian Academy of Sciences,
Sofia-1113, Bulgaria

R. D. Knott
92 Pennine Road, Horwich,
Bolton, BL6 7HW, United Kingdom

R. L. Ollerton
University of Western Sydney, Penrith Campus DC1797, Australia

A. G. Shannon
Warrane College, The University of New South Wales, 1465 &
KvB Institute of Technology, North Sydney, NSW, 2060, Australia


This paper continues our study of Fibonacci inequalities. For the set An = {Fn−1, 4Fn−2, …, (n−2)2F2} with kth element given by ak = k2Fn−k, it is proved that the unique maximal element is given by a* = a4 = 16Fn−4, n ≥ 9.

AMS Classification

  • 11B39


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  2. S. Vajda, Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications. Chichester: Ellis Horwood, 1989.
  3. N. Gauthier, “Two Fibonacci Sums – a Variation.” Mathematical Gazette. 81 (1997): 85-88.
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  6. Wolfram Research Inc
  7. Kiyota Ozeki, “On Weighted Fibonacci and Lucas Sums.” The Fibonacci Quarterly, 43 (2005): 104-107.

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Cite this paper

Atanassov, K. T., Knot, R. D., Ollerton, R. L., & Shannon, A. G. (2006). An extremal problem related to the Fibonacci sequence. Notes on Number Theory and Discrete Mathematics, 12(2), 13-20.

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