Integers with a maximal number of Fibonacci representations
Petra Kocábová; Zuzana Masáková; Edita Pelantová
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)
- Volume: 39, Issue: 2, page 343-359
- ISSN: 0988-3754
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topKocábová, Petra, Masáková, Zuzana, and Pelantová, Edita. "Integers with a maximal number of Fibonacci representations." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.2 (2005): 343-359. <http://eudml.org/doc/244616>.
@article{Kocábová2005,
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 $F_k$. We determine the maximum and mean values of $R(n)$ for $F_k\le n<F_\{k+1\}$.},
author = {Kocábová, Petra, Masáková, Zuzana, Pelantová, Edita},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {Fibonacci numbers; Zeckendorf representation},
language = {eng},
number = {2},
pages = {343-359},
publisher = {EDP-Sciences},
title = {Integers with a maximal number of Fibonacci representations},
url = {http://eudml.org/doc/244616},
volume = {39},
year = {2005},
}
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 - Informatique Théorique et Applications
PY - 2005
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 $F_k$. We determine the maximum and mean values of $R(n)$ for $F_k\le n<F_{k+1}$.
LA - eng
KW - Fibonacci numbers; Zeckendorf representation
UR - http://eudml.org/doc/244616
ER -
References
top- [1] J. Berstel, An exercise on Fibonacci representations. RAIRO-Inf. Theor. Appl. 35 (2001) 491–498. Zbl1005.68119
- [2] M. Bicknell-Johnson, The smallest positive integer having 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 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). MR2094251
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