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

2, 1, 2, 3, 2, 3, 4, 12, 14, 17, 14, 13, 12, 20, 32, 406, 538, 703, 842, 1085, 1310, 1465, 1544, 1570, 1968, 2132, 2000, 2480, 2176, 2816, 4096, 1060280

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..32.

D. Gabric, S. Holub, and J. Shallit, Generalized de Bruijn words and the state complexity of conjugate sets, arXiv:1903.05442 [cs.FL], March 13 2019.

Formula

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

Crossrefs

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

Cf. A070939.

Sequence in context: A174832 A076827 A165477 * A119994 A029167 A161103

Adjacent sequences: A318684 A318685 A318686 * A318688 A318689 A318690

Keyword

nonn,more

Author

Jeffrey Shallit, Aug 31 2018

Status

approved