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Generating functions for the digital sum and other digit counting sequences

*Franklin T. Adams-Watters*.

*Frank Ruskey*,
Department of Computer Science,
University of Victoria, Canada.

### Abstract:

A numeration system associates a unique string, *X*(*n*),
with each positive integer *n*, where each string is
over the same finite alphabet.
Various digit counting statistics of *X*(*n*) are of interest.
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.

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