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 A215327 Smooth necklaces with 3 colors. 8
 1, 3, 5, 8, 15, 27, 58, 115, 252, 541, 1196, 2629, 5894, 13156, 29667, 66978, 151966, 345497, 788396, 1802678, 4133161, 9495317, 21861393, 50423468, 116514553 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS We call a necklace (x[1],x[2],...,x[n]) smooth if abs(x[k]-x[k-1]) <= 1 for 2<=k<=n. All binary necklaces (2 colors, A000031) are necessarily smooth. LINKS EXAMPLE The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 4 with 3 colors (using symbols ".", "1", and "2") are:     ....   1       .  N     ...1   4    ...1  N L     ..1.   3     .1.     ..11   4    ..11  N L     ..12   4    ..12  N L     .1.1   2      .1  N     .11.   3     11.     .111   4    .111  N L     .112   4    .112  N L     .121   4    .121  N L     .122   4    .122  N L     1111   1       1  N     1112   4    1112  N L     1121   3     121     1122   4    1122  N L     1212   2      12  N     1221   3     221     1222   4    1222  N L     2222   1       2  N There are 19 pre-necklaces, 15 necklaces, and 10 Lyndon words. So a(4) = 15. CROSSREFS Cf. A001867 (necklaces, 3 colors), A215328 (smooth Lyndon words, 3 colors). Sequence in context: A193147 A052977 A191633 * A208723 A285010 A099846 Adjacent sequences:  A215324 A215325 A215326 * A215328 A215329 A215330 KEYWORD nonn,more AUTHOR Joerg Arndt, Aug 08 2012 STATUS approved

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