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A002076
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Number of equivalence classes of base-3 necklaces of length n, where necklaces are considered equivalent under both rotations as well as permutations of the symbols.
(Formerly M0761 N0288)
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6
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1, 2, 3, 6, 9, 26, 53, 146, 369, 1002, 2685, 7434, 20441, 57046, 159451, 448686, 1266081, 3588002, 10195277, 29058526, 83018783, 237740670, 682196949, 1961331314, 5648590737, 16294052602, 47071590147, 136171497650
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| N. J. Fine, Classes of periodic sequences, Illinois J. Math., 2 (1958), 285-302.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Maple code for this and related sequences
Index entries for sequences related to necklaces
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FORMULA
| Reference gives formula.
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EXAMPLE
| E.g. a(2) = 2 as there are two equivalence classes of the 9 strings {00,01,02,10,11,12,20,21,22 }: {00,11,22} form one equivalence class and {01,02,10,12,20,21} form the other. To see that (for example) 01 and 02 are equivalent, rotate 01 to 10 and then subtract 1 mod 3 from each element in 10 to get 02.
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CROSSREFS
| Cf. A000013, A000048, A002075.
Sequence in context: A056353 A111274 A133385 * A145761 A071714 A077753
Adjacent sequences: A002073 A002074 A002075 * A002077 A002078 A002079
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description and more terms from Mark Weston (mweston(AT)uvic.ca), Oct 06 2001
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