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 A215331 Smooth necklaces with 5 colors. 1

%I #12 Jun 17 2019 05:46:55

%S 1,5,9,16,35,76,190,455,1156,2911,7438,18992,48902,125968,325975,

%T 845202,2197690,5725854,14951308,39110371,102490649,269002564,

%U 707096093,1861183847,4905172383,12942843424

%N Smooth necklaces with 5 colors.

%C We call a necklace (x[1],x[2],...,x[n]) smooth if abs(x[k]-x[k-1]) <= 1 for 2<=k<=n.

%e The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 4 with 4 colors (using symbols ".", "1", "2", "3", and "4") are:

%e .... 1 . N

%e ...1 4 ...1 N L

%e ..1. 3 .1.

%e ..11 4 ..11 N L

%e ..12 4 ..12 N L

%e .1.1 2 .1 N

%e .11. 3 11.

%e .111 4 .111 N L

%e .112 4 .112 N L

%e .121 4 .121 N L

%e .122 4 .122 N L

%e .123 4 .123 N L

%e 1111 1 1 N

%e 1112 4 1112 N L

%e 1121 3 121

%e 1122 4 1122 N L

%e 1123 4 1123 N L

%e 1212 2 12 N

%e 1221 3 221

%e 1222 4 1222 N L

%e 1223 4 1223 N L

%e 1232 4 1232 N L

%e 1233 4 1233 N L

%e 1234 4 1234 N L

%e 2222 1 2 N

%e 2223 4 2223 N L

%e 2232 3 232

%e 2233 4 2233 N L

%e 2234 4 2234 N L

%e 2323 2 23 N

%e 2332 3 332

%e 2333 4 2333 N L

%e 2334 4 2334 N L

%e 2343 4 2343 N L

%e 2344 4 2344 N L

%e 3333 1 3 N

%e 3334 4 3334 N L

%e 3343 3 343

%e 3344 4 3344 N L

%e 3434 2 34 N

%e 3443 3 443

%e 3444 4 3444 N L

%e 4444 1 4 N

%e There are 43 pre-necklaces, 35 necklaces, and 26 Lyndon words.

%e So a(4) = 35.

%Y Cf. A215327 (smooth necklaces, 3 colors) A215328 (smooth Lyndon words, 3 colors).

%K nonn,more

%O 0,2

%A _Joerg Arndt_, Aug 08 2012

%E More terms from _Joerg Arndt_, Jun 17 2019

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Last modified September 7 09:52 EDT 2024. Contains 375730 sequences. (Running on oeis4.)