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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, 269666605, 625108573, 1451128479, 3373267275, 7851415838, 18296568717 (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 Table of n, a(n) for n=0..30. 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 A352917 Adjacent sequences: A215324 A215325 A215326 * A215328 A215329 A215330 KEYWORD nonn AUTHOR Joerg Arndt, Aug 08 2012 EXTENSIONS More terms from Joerg Arndt, Jun 17 2019 STATUS approved

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Last modified August 12 19:26 EDT 2024. Contains 375113 sequences. (Running on oeis4.)