

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): 41974199 (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: A063698 A287466 A288014 * A250397 A224074 A136615
Adjacent sequences: A179674 A179675 A179676 * A179678 A179679 A179680


KEYWORD

nonn,more


AUTHOR

Jeffrey Shallit, Jan 09 2011


STATUS

approved



