We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.
@article{ITA_2001__35_6_491_0,
author = {Berstel, Jean},
title = {An exercise on {Fibonacci} representations},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {491--498},
year = {2001},
publisher = {EDP Sciences},
volume = {35},
number = {6},
mrnumber = {1922290},
zbl = {1005.68119},
language = {en},
url = {https://www.numdam.org/item/ITA_2001__35_6_491_0/}
}
TY - JOUR AU - Berstel, Jean TI - An exercise on Fibonacci representations JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2001 SP - 491 EP - 498 VL - 35 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/item/ITA_2001__35_6_491_0/ LA - en ID - ITA_2001__35_6_491_0 ER -
%0 Journal Article %A Berstel, Jean %T An exercise on Fibonacci representations %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2001 %P 491-498 %V 35 %N 6 %I EDP Sciences %U https://www.numdam.org/item/ITA_2001__35_6_491_0/ %G en %F ITA_2001__35_6_491_0
Berstel, Jean. An exercise on Fibonacci representations. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 6, pp. 491-498. https://www.numdam.org/item/ITA_2001__35_6_491_0/
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