OFFSET
1,3
COMMENTS
A Lyndon word is an aperiodic word that is lexicographically least in its conjugacy class (of cyclic shifts). A conjugate is a cyclic shift. Hamming distance is the number of positions in which two strings differ.
FORMULA
a(n) = A179674(n) / n. - Falk Hüffner, Aug 15 2021
EXAMPLE
a(7) = 14, because there are 18 binary Lyndon words of length 7, and all but the following 4 have a conjugate at Hamming distance 2: 0001011, 0001101, 0010111, 0011101.
From Joerg Arndt, Jun 21 2013: (Start)
There are a(8) = 20 Lyndon words of length 8 that have a conjugate at Hamming distance 2 (dots for zeros):
ct: word conjugate word XOR conjugate
01: 1....... .1...... 11......
02: 11...... .11..... 1.1.....
03: 1.1..... ..1.1... 1...1...
04: 111..... .111.... 1..1....
05: 1..1.... ...1..1. 1.....1.
06: 1111.... .1111... 1...1...
07: 11..1... 1...11.. .1...1..
08: 1.1.1... ..1.1.1. 1.....1.
09: 1..11... 1...1..1 ...1...1
10: 11111... .11111.. 1....1..
11: 1.1..1.. 1..1.1.. ..11....
12: 1.11.1.. 1..1.11. ..1...1.
13: 111.11.. 11..111. ..1...1.
14: 11.111.. 11..11.1 ...1...1
15: 111111.. .111111. 1.....1.
16: 111.1.1. 1.111.1. .1.1....
17: 11.11.1. .1.11.11 1......1
18: 11111.1. 1.11111. .1...1..
19: 1111.11. 11.1111. ..1.1...
20: 1111111. .1111111 1......1
(End)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Jun 21 2013
EXTENSIONS
More terms from Joerg Arndt, Jun 21 2013 and Jun 26 2013
STATUS
approved