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A318687 Number of length-n circular binary words having exactly n distinct blocks of length floor(log_2(n)) + 1 (A070939). 1

%I

%S 2,1,2,3,2,3,4,12,14,17,14,13,12,20,32,406,538,703,842,1085,1310,1465,

%T 1544,1570,1968,2132,2000,2480,2176,2816,4096,1060280

%N Number of length-n circular binary words having exactly n distinct blocks of length floor(log_2(n)) + 1 (A070939).

%C A "circular word" (a.k.a. "necklace") is one that wraps around from the end to the beginning. The words are counted up to an equivalence where two circular words are the same if one is a cyclic shift of the other.

%H D. Gabric, S. Holub, and J. Shallit, <a href="https://arxiv.org/abs/1903.05442">Generalized de Bruijn words and the state complexity of conjugate sets</a>, arXiv:1903.05442 [cs.FL], March 13 2019.

%F a(2^n-1) = 2^(2^(n-1)-n+1) since A317586(2^n) = 2^(2^(n-1)-n) and A317586(2^n-1) = A317586(2^n+1) = 2*A317586(2^n) = 2^(2^(n-1)-n+1). - _Altug Alkan_, Sep 05 2018

%Y Cf. A317586, which studies a similar quantity for two different lengths of blocks.

%Y Cf. A070939.

%K nonn,more

%O 1,1

%A _Jeffrey Shallit_, Aug 31 2018

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Last modified April 3 22:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)