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%I #16 Jan 25 2019 08:31:25
%S 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,
%T 14,15,16,16,16,17,17,18,18,19
%N Maximum number of unbordered conjugates for a binary word of length n.
%C 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.
%H T. Harju and D. Nowotka, <a href="https://doi.org/10.1016/j.jcta.2004.07.009">Border correlation of binary words</a>, J. Combin. Theory Ser. A 108 (2004), 331-341.
%e 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.
%K nonn,more
%O 1,2
%A _Jeffrey Shallit_, Jan 10 2019
%E a(25)-a(39) from _Lars Blomberg_, Jan 25 2019
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