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A194942 List of seven normalized ternary Abelian squarefree words. 1

%I #15 Jul 07 2015 22:24:06

%S 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,

%T 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,

%U 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

%N List of seven normalized ternary Abelian squarefree words.

%C 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}.

%C 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.

%H V. Keränen, <a href="http://south.rotol.ramk.fi/keranen/ias2002/NewAbelianSquare-FreeDT0L-LanguagesOver4Letters.nb">New Abelian Square-Free DT0L-Languages over 4 Letters</a>

%e The rows are:

%e {{0}},

%e {{0, 1}},

%e {{0, 1, 0}, {0, 1, 2}},

%e {{0, 1, 0, 2}, {0, 1, 2, 0}, {0, 1, 2, 1}},

%e {{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}},

%e {{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}},

%e {{0, 1, 0, 2, 0, 1, 0}, {0, 1, 0, 2, 1, 0, 1}, {0, 1, 2, 1, 0, 1, 2}}

%Y Cf. A194923 (includes non-normalized sequences).

%K nonn,fini,full,tabf

%O 1,9

%A _Franklin T. Adams-Watters_, Sep 05 2011

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Last modified April 25 10:01 EDT 2024. Contains 371967 sequences. (Running on oeis4.)