

A066297


Number of ternary squarefree necklaces.


1



1, 3, 6, 6, 12, 0, 18, 0, 24, 0, 0, 66, 72, 78, 0, 30, 48, 0, 252, 228, 300, 42, 462, 690, 720, 750, 702, 810, 1260, 2088, 3870, 5022, 5568, 4752, 5916, 10920, 16416
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OFFSET

0,2


COMMENTS

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).
Several similar sequences (with same zeros) can be constructed from equivalence classes of the loops.
Higher terms: a(n) > 0 for 30 < n <= 56; no zeros known after a(17).
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


LINKS

Table of n, a(n) for n=0..36.
J. D. Currie, There are ternary circular squarefree words of length n for n >= 18, Elect. J. Combinatorics 9 (2002), Paper N10.


EXAMPLE

a(1)=3, size of {"a","b","c"); a(6)=18, size of {"abacbc","bacbca",...,"cbabca"}.


CROSSREFS

Variant of A006156. See also A001037, A006206.
Sequence in context: A200534 A184284 A287882 * A160713 A279625 A012212
Adjacent sequences: A066294 A066295 A066296 * A066298 A066299 A066300


KEYWORD

hard,nice,nonn,more


AUTHOR

Paul Parsons (paul.parsons6(AT)btinternet.com)


EXTENSIONS

a(31)a(36) from Jeffrey Shallit, Jan 22 2019


STATUS

approved



