A215333 - OEIS

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

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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..22.

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: A356966 A090992 A259215 * A034780 A137165 A087195

Adjacent sequences: A215330 A215331 A215332 * A215334 A215335 A215336

KEYWORD

nonn,more

AUTHOR

Joerg Arndt, Aug 08 2012

EXTENSIONS

More terms from Joerg Arndt, Jun 17 2019

STATUS

approved