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A215333 Smooth necklaces with 7 colors. 2
1, 7, 13, 24, 55, 126, 330, 836, 2232, 5926, 15932, 42849, 116011, 314375, 854952 (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..14.

EXAMPLE

The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 3 with 4 colors (using symbols ".", "1", "2", "3", "4", "5", and "6") are:

    ...   1      .  N

    ..1   3    ..1  N L

    .1.   2     1.

    .11   3    .11  N L

    .12   3    .12  N L

    111   1      1  N

    112   3    112  N L

    121   2     21

    122   3    122  N L

    123   3    123  N L

    222   1      2  N

    223   3    223  N L

    232   2     32

    233   3    233  N L

    234   3    234  N L

    333   1      3  N

    334   3    334  N L

    343   2     43

    344   3    344  N L

    345   3    345  N L

    444   1      4  N

    445   3    445  N L

    454   2     54

    455   3    455  N L

    456   3    456  N L

    555   1      5  N

    556   3    556  N L

    565   2     65

    566   3    566  N L

    666   1      6  N

There are 30 pre-necklaces, 24 necklaces, and 17 Lyndon words.

So a(3) = 24.

CROSSREFS

Cf. A215327 (smooth necklaces with 3 colors).

Sequence in context: A188557 A090992 A259215 * A034780 A137165 A087195

Adjacent sequences:  A215330 A215331 A215332 * A215334 A215335 A215336

KEYWORD

nonn,more

AUTHOR

Joerg Arndt, Aug 08 2012

STATUS

approved

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Last modified November 18 18:46 EST 2017. Contains 294894 sequences.