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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

Table of n, a(n) for n=1..16.

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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Last modified December 18 10:16 EST 2014. Contains 252138 sequences.