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A215331 Smooth necklaces with 5 colors. 1
1, 5, 9, 16, 35, 76, 190, 455, 1156, 2911, 7438, 18992, 48902, 125968, 325975, 845202, 2197690, 5725854 (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.

LINKS

Table of n, a(n) for n=0..17.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A218611 A208669 A062777 * A208725 A272742 A273534

Adjacent sequences:  A215328 A215329 A215330 * A215332 A215333 A215334

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.