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A066297
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Number of ternary squarefree necklaces.
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1
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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a(1)=3, size of {"a","b","c"}; a(6)=18, size of {"abacbc","bacbca",...,"cbabca"}.
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CROSSREFS
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KEYWORD
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hard,nice,nonn,changed
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AUTHOR
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Paul Parsons (paul.parsons6(AT)btinternet.com)
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EXTENSIONS
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STATUS
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approved
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