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Generating Functions for the Digital Sum and Other Digit Counting Sequences
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Franklin T. Adams-Watters

and

Frank Ruskey

University of Victoria

Victoria, BC V8W 3P6

Canada

**Abstract:**

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

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(Concerned with sequences
A000120
A003849
A007895
A014417
A023416
A034968
A053735
A053737
A062756
A065363
A077267
A080791
A081602
A081603
A139351
A139352
A139365
A160380
A160381
A160382
A160383
A160384
A160385.)

Received June 19 2009;
revised version received July 11 2009.
Published in *Journal of Integer Sequences*, July 12 2009.

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