Integers with a maximal number of Fibonacci representations

Petra Kocábová; Zuzana Masáková; Edita Pelantová

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 39, Issue: 2, page 343-359
  • ISSN: 0988-3754

Abstract

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We study the properties of the function R(n) which determines the number of representations of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and mean values of R(n) for Fk ≤ n < Fk+1.

How to cite

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Kocábová, Petra, Masáková, Zuzana, and Pelantová, Edita. "Integers with a maximal number of Fibonacci representations." RAIRO - Theoretical Informatics and Applications 39.2 (2010): 343-359. <http://eudml.org/doc/92770>.

@article{Kocábová2010,
abstract = { We study the properties of the function R(n) which determines the number of representations of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and mean values of R(n) for Fk ≤ n < Fk+1. },
author = {Kocábová, Petra, Masáková, Zuzana, Pelantová, Edita},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Fibonacci numbers; Zeckendorf representation.; Zeckendorf representation},
language = {eng},
month = {3},
number = {2},
pages = {343-359},
publisher = {EDP Sciences},
title = {Integers with a maximal number of Fibonacci representations},
url = {http://eudml.org/doc/92770},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Kocábová, Petra
AU - Masáková, Zuzana
AU - Pelantová, Edita
TI - Integers with a maximal number of Fibonacci representations
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 2
SP - 343
EP - 359
AB - We study the properties of the function R(n) which determines the number of representations of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and mean values of R(n) for Fk ≤ n < Fk+1.
LA - eng
KW - Fibonacci numbers; Zeckendorf representation.; Zeckendorf representation
UR - http://eudml.org/doc/92770
ER -

References

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  1. J. Berstel, An exercise on Fibonacci representations. RAIRO-Inf. Theor. Appl.35 (2001) 491–498.  
  2. M. Bicknell-Johnson, The smallest positive integer having Fk representations as sums of distinct Fibonacci numbers, in Applications of Fibonacci numbers. Vol. 8, Kluwer Acad. Publ., Dordrecht (1999) 47–52.  Zbl0957.11011
  3. M. Bicknell-Johnson and D.C. Fielder, The number of representations of N using distinct Fibonacci numbers, counted by recursive formulas. Fibonacci Quart.37 (1999) 47–60.  Zbl0949.11010
  4. M. Edson and L. Zamboni, On representations of positive integers in the Fibonacci base. Preprint University of North Texas (2003).  Zbl1074.11007

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