A215333 Smooth necklaces with 7 colors.

1, 7, 13, 24, 55, 126, 330, 836, 2232, 5926, 15932, 42849, 116011, 314375, 854952, 2329162, 6359574, 17393334, 47653952, 130752976, 359275056, 988458426, 2722803495

Offset: 0

Author

Joerg Arndt, Aug 08 2012

Keywords

• nonn
• more

Comments

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

Examples

			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).

Extensions

More terms from Joerg Arndt, Jun 17 2019