This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A215327 #14 Jun 17 2019 05:36:32 %S A215327 1,3,5,8,15,27,58,115,252,541,1196,2629,5894,13156,29667,66978,151966, %T A215327 345497,788396,1802678,4133161,9495317,21861393,50423468,116514553, %U A215327 269666605,625108573,1451128479,3373267275,7851415838,18296568717 %N A215327 Smooth necklaces with 3 colors. %C A215327 We call a necklace (x[1],x[2],...,x[n]) smooth if abs(x[k]-x[k-1]) <= 1 for 2<=k<=n. %C A215327 All binary necklaces (2 colors, A000031) are necessarily smooth. %e A215327 The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 4 with 3 colors (using symbols ".", "1", and "2") are: %e A215327 .... 1 . N %e A215327 ...1 4 ...1 N L %e A215327 ..1. 3 .1. %e A215327 ..11 4 ..11 N L %e A215327 ..12 4 ..12 N L %e A215327 .1.1 2 .1 N %e A215327 .11. 3 11. %e A215327 .111 4 .111 N L %e A215327 .112 4 .112 N L %e A215327 .121 4 .121 N L %e A215327 .122 4 .122 N L %e A215327 1111 1 1 N %e A215327 1112 4 1112 N L %e A215327 1121 3 121 %e A215327 1122 4 1122 N L %e A215327 1212 2 12 N %e A215327 1221 3 221 %e A215327 1222 4 1222 N L %e A215327 2222 1 2 N %e A215327 There are 19 pre-necklaces, 15 necklaces, and 10 Lyndon words. %e A215327 So a(4) = 15. %Y A215327 Cf. A001867 (necklaces, 3 colors), A215328 (smooth Lyndon words, 3 colors). %K A215327 nonn %O A215327 0,2 %A A215327 _Joerg Arndt_, Aug 08 2012 %E A215327 More terms from _Joerg Arndt_, Jun 17 2019