# 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

## Access Full Article

top## Abstract

top## How to cite

topKocábová, 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

top- J. Berstel, An exercise on Fibonacci representations. RAIRO-Inf. Theor. Appl.35 (2001) 491–498.
- 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
- 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
- M. Edson and L. Zamboni, On representations of positive integers in the Fibonacci base. Preprint University of North Texas (2003). Zbl1074.11007