Integers with a maximal number of Fibonacci representations
Kocábová, Petra ; Masáková, Zuzana ; Pelantová, Edita
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005), p. 343-359 / Harvested from Numdam
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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 F k . We determine the maximum and mean values of R(n) for F k ≤n<F k+1 .

Publié le : 2005-01-01
DOI : https://doi.org/10.1051/ita:2005022
Classification:  11A67,  11B39 
@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},
     volume = {39},
     year = {2005},
     pages = {343-359},
     doi = {10.1051/ita:2005022},
     mrnumber = {2142117},
     zbl = {1074.11008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 343-359. doi : 10.1051/ita:2005022. http://gdmltest.u-ga.fr/item/ITA_2005__39_2_343_0/

[1] J. Berstel, An exercise on Fibonacci representations. RAIRO-Inf. Theor. Appl. 35 (2001) 491-498. | Numdam | Zbl 1005.68119

[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 0957.11011

[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. | Zbl 0949.11010

[4] M. Edson and L. Zamboni, On representations of positive integers in the Fibonacci base. Preprint University of North Texas (2003). | MR 2094251