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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 (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..24.

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 A099846

Adjacent sequences:  A215324 A215325 A215326 * A215328 A215329 A215330

KEYWORD

nonn,more

AUTHOR

Joerg Arndt, Aug 08 2012

STATUS

approved

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Last modified November 18 17:56 EST 2017. Contains 294894 sequences.