login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215329 Smooth necklaces with 4 colors. 2
1, 4, 7, 12, 25, 51, 121, 272, 656, 1563, 3794, 9193, 22529, 55189, 136025, 335942, 832605, 2068070, 5150558, 12852754, 32139908, 80509629, 202016993, 507669052, 1277595853, 3219366640, 8122296152 (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
EXAMPLE
The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 4 with 4 colors (using symbols ".", "1", "2", and "3") 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
2222 1 2 N
2223 4 2223 N L
2232 3 232
2233 4 2233 N L
2323 2 23 N
2332 3 332
2333 4 2333 N L
3333 1 3 N
There are 31 pre-necklaces, 25 necklaces, and 18 Lyndon words.
So a(4) = 25.
CROSSREFS
Cf. A215327 (smooth necklaces, 3 colors)
Sequence in context: A322619 A299900 A373094 * A208724 A183336 A102953
KEYWORD
nonn,more
AUTHOR
Joerg Arndt, Aug 08 2012
EXTENSIONS
More terms from Joerg Arndt, Jun 17 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 03:47 EDT 2024. Contains 374544 sequences. (Running on oeis4.)