A194942 - OEIS

A194942

List of seven normalized ternary Abelian squarefree words.

0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 0, 1, 2, 1, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 2, 0, 1, 2, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 0, 0, 1, 0, 2, 1, 2, 0, 1, 2, 0, 1, 0, 0, 1, 2, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2

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OFFSET

1,9

COMMENTS

Lexicographically ordered list of words of increasing length L=1,2,3,... over the alphabet {0,1,2}, without those which contain two adjacent subsequences with the same multiset of symbols, regardless of internal order. Only those words where the symbols appear in order are included; e.g., {0, 1, 0, 2}, but not {0, 2, 0, 1} or {1, 2, 1, 0}.

The row lengths in number of sequences are 1, 1, 2, 3, 5, 5, 3, for total row lengths of 1, 2, 6, 12, 25, 30, 21.

LINKS

Table of n, a(n) for n=1..97.

V. Keränen, New Abelian Square-Free DT0L-Languages over 4 Letters

EXAMPLE

The rows are:

{{0}},

{{0, 1}},

{{0, 1, 0}, {0, 1, 2}},

{{0, 1, 0, 2}, {0, 1, 2, 0}, {0, 1, 2, 1}},

{{0, 1, 0, 2, 0}, {0, 1, 0, 2, 1}, {0, 1, 2, 0, 1}, {0, 1, 2, 0, 2}, {0, 1, 2, 1, 0}},

{{0, 1, 0, 2, 0, 1}, {0, 1, 0, 2, 1, 0}, {0, 1, 0, 2, 1, 2}, {0, 1, 2, 0, 1, 0}, {0, 1, 2, 1, 0, 1}},