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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 (list; graph; refs; listen; history; text; internal format)
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 length-n 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), 331-341.

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

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Last modified November 18 02:20 EST 2019. Contains 329243 sequences. (Running on oeis4.)