Journal of Integer Sequences, Vol. 12 (2009), Article 09.5.6

Generating Functions for the Digital Sum and Other Digit Counting Sequences

Franklin T. Adams-Watters


Frank Ruskey
University of Victoria
Victoria, BC V8W 3P6


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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