Integers with a maximal number of Fibonacci representations
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 2, pp. 343-359.

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 n<F k+1 .

DOI : 10.1051/ita:2005022
Classification : 11A67, 11B39
Mots clés : Fibonacci numbers, Zeckendorf representation
@article{ITA_2005__39_2_343_0,
     author = {Koc\'abov\'a, Petra and Mas\'akov\'a, Zuzana and Pelantov\'a, Edita},
     title = {Integers with a maximal number of {Fibonacci} representations},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {343--359},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {2},
     year = {2005},
     doi = {10.1051/ita:2005022},
     mrnumber = {2142117},
     zbl = {1074.11008},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita:2005022/}
}
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
SP  - 343
EP  - 359
VL  - 39
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ita:2005022/
DO  - 10.1051/ita:2005022
LA  - en
ID  - ITA_2005__39_2_343_0
ER  - 
%0 Journal Article
%A Kocábová, Petra
%A Masáková, Zuzana
%A Pelantová, Edita
%T Integers with a maximal number of Fibonacci representations
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2005
%P 343-359
%V 39
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ita:2005022/
%R 10.1051/ita:2005022
%G en
%F ITA_2005__39_2_343_0
Kocábová, Petra; Masáková, Zuzana; Pelantová, Edita. Integers with a maximal number of Fibonacci representations. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 2, pp. 343-359. doi : 10.1051/ita:2005022. http://archive.numdam.org/articles/10.1051/ita:2005022/

[1] J. Berstel, An exercise on Fibonacci representations. RAIRO-Inf. Theor. Appl. 35 (2001) 491-498. | Numdam | Zbl

[2] M. Bicknell-Johnson, The smallest positive integer having F k representations as sums of distinct Fibonacci numbers, in Applications of Fibonacci numbers. Vol. 8, Kluwer Acad. Publ., Dordrecht (1999) 47-52. | Zbl

[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. | Zbl

[4] M. Edson and L. Zamboni, On representations of positive integers in the Fibonacci base. Preprint University of North Texas (2003). | MR

Cité par Sources :