A066297 - OEIS

A066297

Number of ternary squarefree necklaces.

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, 18870, 21660, 23556, 34320, 51414, 75852, 93654, 108372, 126360, 172914, 245058, 343872

(list; graph; refs; listen; history; text; internal format)

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..48.

J. D. Currie, There are ternary circular square-free 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: A138743 A184284 A287882 * A160713 A279625 A012212

Adjacent sequences: A066294 A066295 A066296 * A066298 A066299 A066300

KEYWORD

hard,nice,nonn

AUTHOR

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

EXTENSIONS

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

a(37)-a(48) from Sean A. Irvine, Oct 07 2023

STATUS

approved