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A215331
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Smooth necklaces with 5 colors.
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1
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1, 5, 9, 16, 35, 76, 190, 455, 1156, 2911, 7438, 18992, 48902, 125968, 325975, 845202, 2197690, 5725854, 14951308, 39110371, 102490649, 269002564, 707096093, 1861183847, 4905172383, 12942843424
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listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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We call a necklace (x[1],x[2],...,x[n]) smooth if abs(x[k]-x[k-1]) <= 1 for 2<=k<=n.
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LINKS
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EXAMPLE
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The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 4 with 4 colors (using symbols ".", "1", "2", "3", and "4") 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
1234 4 1234 N L
2222 1 2 N
2223 4 2223 N L
2232 3 232
2233 4 2233 N L
2234 4 2234 N L
2323 2 23 N
2332 3 332
2333 4 2333 N L
2334 4 2334 N L
2343 4 2343 N L
2344 4 2344 N L
3333 1 3 N
3334 4 3334 N L
3343 3 343
3344 4 3344 N L
3434 2 34 N
3443 3 443
3444 4 3444 N L
4444 1 4 N
There are 43 pre-necklaces, 35 necklaces, and 26 Lyndon words.
So a(4) = 35.
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CROSSREFS
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Cf. A215327 (smooth necklaces, 3 colors) A215328 (smooth Lyndon words, 3 colors).
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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