

A321162


Maximum number of unbordered conjugates for a binary word of length n.


1



1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 9, 9, 10, 10, 11, 12, 12, 12, 13, 13, 14, 14, 15, 16, 16, 16, 17, 17, 18, 18, 19
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OFFSET

1,2


COMMENTS

Two words are conjugate if one is a cyclic shift of the other, such as "enlist" and "listen". A word w is bordered if it has a nonempty prefix that is also a suffix (and not equal to w), such as the word "entanglement". Harju and Nowotka show that for lengthn binary words, at most n/2 unbordered conjugates are possible.


LINKS

Table of n, a(n) for n=1..39.
T. Harju and D. Nowotka, Border correlation of binary words, J. Combin. Theory Ser. A 108 (2004), 331341.


EXAMPLE

For n = 10, the word 0000101101 has 10 distinct conjugates, but only 4 of them are unbordered: {0000101101, 1011010000, 1101000010, 0100001011}. This is maximum for n = 10.


CROSSREFS

Sequence in context: A090701 A056970 A212218 * A008668 A225643 A116563
Adjacent sequences: A321159 A321160 A321161 * A321163 A321164 A321165


KEYWORD

nonn,more


AUTHOR

Jeffrey Shallit, Jan 10 2019


EXTENSIONS

a(25)a(39) from Lars Blomberg, Jan 25 2019


STATUS

approved



