Geodesic
Generating functions for the digital sum and other digit counting sequences
Journal of integer sequences, Tome 12 (2009) no. 5
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 
@article{JIS_2009__12_5_a7,
     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},
     year = {2009},
     volume = {12},
     number = {5},
     zbl = {1213.11023},
     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/