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A179677
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Number of binary sequences of length n having exactly one conjugate at Hamming distance 2
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1
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0, 2, 0, 0, 0, 12, 0, 32, 0, 140, 0, 264, 0, 868, 0, 1792
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OFFSET
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1,2
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COMMENTS
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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.
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REFERENCES
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J. Shallit: Hamming distance for conjugates. Discrete Mathematics 309(12): 4197-4199 (2009)
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LINKS
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Table of n, a(n) for n=1..16.
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A181502 A223154 A063698 * A224074 A136615 A209401
Adjacent sequences: A179674 A179675 A179676 * A179678 A179679 A179680
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KEYWORD
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nonn
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AUTHOR
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Jeffrey Shallit, Jan 09 2011
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STATUS
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approved
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