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 A179677 Number of binary sequences of length n having exactly one conjugate at Hamming distance 2 1
 0, 2, 0, 0, 0, 12, 0, 32, 0, 140, 0, 264, 0, 868, 0, 1792 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The conjugate of a binary sequence is a cyclic shift.  For example, 001011 and 110010 are conjugates because if you rotate the first 4 places to the left, you get the second. The Hamming distance is the number of bits that are different. REFERENCES J. Shallit: Hamming distance for conjugates. Discrete Mathematics 309(12): 4197-4199 (2009) LINKS EXAMPLE a(6) = 12, with examples being 001011, 001101, 010011, 010110, 011001, 011010, and their complements (0's and 1's interchanged).  The conjugates of 001011 are: 010110, 101100, 011001, 110010, and 100101, which have Hamming distances 4, 4, 2, 4, and 4, respectively, so exactly one has distance 2. CROSSREFS Sequence in context: A181502 A223154 A063698 * A250397 A224074 A136615 Adjacent sequences:  A179674 A179675 A179676 * A179678 A179679 A179680 KEYWORD nonn,more AUTHOR Jeffrey Shallit, Jan 09 2011 STATUS approved

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