Search: id:A002076
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%I A002076 M0761 N0288
%S A002076 1,2,3,6,9,26,53,146,369,1002,2685,7434,20441,57046,159451,448686,
%T A002076 1266081,3588002,10195277,29058526,83018783,237740670,682196949,
%U A002076 1961331314,5648590737,16294052602,47071590147,136171497650
%N A002076 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.
%D A002076 N. J. Fine, Classes of periodic sequences, Illinois J. Math., 2 (1958), 
               285-302.
%D A002076 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002076 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002076 N. J. A. Sloane, <a href="a000013.txt">Maple code for this and related 
               sequences</a>
%H A002076 <a href="Sindx_Ne.html#necklaces">Index entries for sequences related 
               to necklaces</a>
%F A002076 Reference gives formula.
%e A002076 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.
%Y A002076 Cf. A000013, A000048, A002075.
%Y A002076 Sequence in context: A056353 A111274 A133385 this_sequence A145761 A071714 
               A077753
%Y A002076 Adjacent sequences: A002073 A002074 A002075 this_sequence A002077 A002078 
               A002079
%K A002076 nonn,easy,nice
%O A002076 1,2
%A A002076 N. J. A. Sloane (njas(AT)research.att.com).
%E A002076 Better description and more terms from Mark Weston (mweston(AT)uvic.ca), 
               Oct 06 2001

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