cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A066297 Number of ternary squarefree necklaces.

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%I A066297 #38 Aug 18 2024 19:02:39
%S A066297 1,3,6,6,12,0,18,0,24,0,0,66,72,78,0,30,48,0,252,228,300,42,462,690,
%T A066297 720,750,702,810,1260,2088,3870,5022,5568,4752,5916,10920,16416,18870,
%U A066297 21660,23556,34320,51414,75852,93654,108372,126360,172914,245058,343872
%N A066297 Number of ternary squarefree necklaces.
%C A066297 A square is an adjacent pair of repeats, e.g., "aa" or "abcabc". A necklace is a word that may be rotated before being tested (for squares).
%C A066297 Several similar sequences (with same zeros) can be constructed from equivalence classes of the loops.
%C A066297 Higher terms: a(n) > 0 for 30 < n <= 56; no zeros known after a(17).
%C A066297 This is also the number of ternary "circular" squarefree words.  The Currie paper proves no 0 entries after a(17). - _Jeffrey Shallit_, Jul 11 2012
%H A066297 J. D. Currie, <a href="https://doi.org/10.37236/1671">There are ternary circular square-free words of length n for n >= 18</a>, Elect. J. Combinatorics 9 (2002), Paper N10.
%e A066297 a(1)=3, size of {"a","b","c"}; a(6)=18, size of {"abacbc","bacbca",...,"cbabca"}.
%Y A066297 Variant of A006156. See also A001037, A006206.
%K A066297 hard,nice,nonn
%O A066297 0,2
%A A066297 Paul Parsons (paul.parsons6(AT)btinternet.com)
%E A066297 a(31)-a(36) from _Jeffrey Shallit_, Jan 22 2019
%E A066297 a(37)-a(48) from _Sean A. Irvine_, Oct 07 2023