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A recursive formula for the Kolakoski sequence A000002. (English) Zbl 1104.11012
Recall that the Kolakoski sequence in the (unique) sequence starting with 1 which is equal to the sequence of its runlength on the alphabet \(\{1,2\}\), i.e., the sequence \(1221121221\dots\). The author proposes a recursive formula for the \(n\)th term of this sequence as well as for the number of \(1\)’s in its first \(n\) terms and the sum of its first \(n\) terms.

MSC:
11B83 Special sequences and polynomials
11Y55 Calculation of integer sequences
Software:
OEIS
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