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A226893 Number of binary Lyndon words of length n having a conjugate at Hamming distance 2. 0
0, 1, 2, 3, 6, 9, 14, 20, 26, 40, 42, 72, 62, 123, 102, 208, 114, 405, 146, 668, 290, 1201, 222, 2504, 316, 4356, 800, 8580, 366, 17866, 422, 33312, 2514, 66010, 990, 135960, 614, 262749, 8870, 526256, 762, 1066044, 842 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..43.

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

Cf. A001037.

Sequence in context: A061925 A073736 A101593 * A084628 A002096 A094055

Adjacent sequences:  A226890 A226891 A226892 * A226894 A226895 A226896

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Jun 21 2013

EXTENSIONS

More terms from Joerg Arndt, Jun 21 2013 and Jun 26 2013

STATUS

approved

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Last modified November 23 19:00 EST 2017. Contains 295128 sequences.