A321166 Maximum number of overlap-free conjugates of a length-n binary word.

1, 2, 3, 4, 4, 6, 6, 8, 5, 7, 4, 12, 5, 11, 6, 16, 4, 9, 6, 13, 6, 7, 6, 24, 6, 8, 5, 21, 5, 11, 6, 32, 5, 7, 6

Offset

1,2

Comments

Two words are conjugates if one is a cyclic shift of the other. A word is overlap-free if it contains no block of the form axaxa, where a is a single letter and x is a (possibly empty) block.

Links

Table of n, a(n) for n=1..35.

T. Harju and D. Nowotka, Border correlation of binary words, J. Combin. Theory Ser. A 108 (2004), 331-341.

Example

The word w = 01001011010 has 4 overlap-free conjugates:  namely, w itself and {10010110100, 00101101001, 01011010010}. This is maximal for n = 11.

Crossrefs

Sequence in context: A343912 A262265 A227683 * A092988 A304575 A296421

Adjacent sequences: A321163 A321164 A321165 * A321167 A321168 A321169

Keyword

nonn,more

Author

Jeffrey Shallit, Jan 10 2019

Extensions

a(22)-a(35) from Lars Blomberg, Feb 15 2019

Status

approved