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 A215329 Smooth necklaces with 4 colors. 2
 1, 4, 7, 12, 25, 51, 121, 272, 656, 1563, 3794, 9193, 22529, 55189, 136025, 335942, 832605, 2068070, 5150558, 12852754 (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. LINKS EXAMPLE The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 4 with 4 colors (using symbols ".", "1", "2", and "3") 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     .123   4    .123  N L     1111   1       1  N     1112   4    1112  N L     1121   3     121     1122   4    1122  N L     1123   4    1123  N L     1212   2      12  N     1221   3     221     1222   4    1222  N L     1223   4    1223  N L     1232   4    1232  N L     1233   4    1233  N L     2222   1       2  N     2223   4    2223  N L     2232   3     232     2233   4    2233  N L     2323   2      23  N     2332   3     332     2333   4    2333  N L     3333   1       3  N There are 31 pre-necklaces, 25 necklaces, and 18 Lyndon words. So a(4) = 25. CROSSREFS Cf. A215327 (smooth necklaces, 3 colors) Sequence in context: A123194 A208668 A243860 * A208724 A183336 A102953 Adjacent sequences:  A215326 A215327 A215328 * A215330 A215331 A215332 KEYWORD nonn,more AUTHOR Joerg Arndt, Aug 08 2012 STATUS approved

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