Geodesic
Generating functions for the digital sum and other digit counting sequences
Journal of integer sequences, Tome 12 (2009) no. 5.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A numeration system associates a unique string, $\Xi (n)$, with each positive integer $n$, where each string is over the same finite alphabet. Various digit counting statistics of $\Xi (n)$ are of interest with respect to a numeration system. An example is the digital sum, which is the sum of the digits in the number. We present a unifying framework for deriving identities for the generating functions of such statistics in many of the more popular numeration systems.
Classification : 05A15, 05A10
Keywords: generating function, numeration system, digital sum, sideways addition, digit counting, morphism, factorial base, balanced ternary numbers 
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     author = {Adams-Watters, Franklin T. and Ruskey, Frank},
     title = {Generating functions for the digital sum and other digit counting sequences},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
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     number = {5},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_5_a7/}
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Adams-Watters, Franklin T.; Ruskey, Frank. Generating functions for the digital sum and other digit counting sequences. Journal of integer sequences, Tome 12 (2009) no. 5. http://geodesic.mathdoc.fr/item/JIS_2009__12_5_a7/