Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.7

A Recursive Formula for the Kolakoski Sequence A000002


Bertran Steinsky
Fürbergstrasse 56
5020 Salzburg
Austria

Abstract: We present a recursive formula for the nth term of the Kolakoski sequence. Using this formula, it is easy to find recursions for the number of ones in the first n terms and for the sum of the first n terms of the Kolakoski sequence.

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(Concerned with sequences A000002 A054349 A054353 and A074286 .)

Received January 13 2006; revised version received August 19 2006. Published in Journal of Integer Sequences August 19 2006.

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