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 A215329 #13 Jun 17 2019 07:31:04 %S A215329 1,4,7,12,25,51,121,272,656,1563,3794,9193,22529,55189,136025,335942, %T A215329 832605,2068070,5150558,12852754,32139908,80509629,202016993, %U A215329 507669052,1277595853,3219366640,8122296152 %N A215329 Smooth necklaces with 4 colors. %C A215329 We call a necklace (x[1],x[2],...,x[n]) smooth if abs(x[k]-x[k-1]) <= 1 for 2<=k<=n. %e A215329 The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 4 with 4 colors (using symbols ".", "1", "2", and "3") are: %e A215329 .... 1 . N %e A215329 ...1 4 ...1 N L %e A215329 ..1. 3 .1. %e A215329 ..11 4 ..11 N L %e A215329 ..12 4 ..12 N L %e A215329 .1.1 2 .1 N %e A215329 .11. 3 11. %e A215329 .111 4 .111 N L %e A215329 .112 4 .112 N L %e A215329 .121 4 .121 N L %e A215329 .122 4 .122 N L %e A215329 .123 4 .123 N L %e A215329 1111 1 1 N %e A215329 1112 4 1112 N L %e A215329 1121 3 121 %e A215329 1122 4 1122 N L %e A215329 1123 4 1123 N L %e A215329 1212 2 12 N %e A215329 1221 3 221 %e A215329 1222 4 1222 N L %e A215329 1223 4 1223 N L %e A215329 1232 4 1232 N L %e A215329 1233 4 1233 N L %e A215329 2222 1 2 N %e A215329 2223 4 2223 N L %e A215329 2232 3 232 %e A215329 2233 4 2233 N L %e A215329 2323 2 23 N %e A215329 2332 3 332 %e A215329 2333 4 2333 N L %e A215329 3333 1 3 N %e A215329 There are 31 pre-necklaces, 25 necklaces, and 18 Lyndon words. %e A215329 So a(4) = 25. %Y A215329 Cf. A215327 (smooth necklaces, 3 colors) %K A215329 nonn,more %O A215329 0,2 %A A215329 _Joerg Arndt_, Aug 08 2012 %E A215329 More terms from _Joerg Arndt_, Jun 17 2019