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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 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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