A274451 Number of possible sets of antipower periods for binary strings of length n.

1, 2, 1, 2, 1, 4, 1, 3, 2, 2, 1, 6, 1, 2, 4, 3, 1, 5, 1, 6, 4, 2, 1, 11, 2, 2, 2, 6, 1, 10, 1, 4

Offset

1,2

Comments

An antiperiod of a length-n string x is a divisor l of n such that if you factor x as the concatenation of (n/l) blocks of length l, then all these blocks are distinct.

Links

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

G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, Anti-powers in infinite words, arxiv preprint, 1606.02868v1 [cs.DM], June 9 2016.

Example

For n = 12 there are six possible sets, achieved by the string that follows each:  {12} 000000000000; {6,12} 000000000001; {4,6,12} 000000010010; {4,12} 000001000001; {3,4,6,12} 000001010011; {3,6,12} 000001010101.

Crossrefs

Cf. A274409, A274449, A274450.

Sequence in context: A256608 A279186 A164799 * A193787 A072614 A287597

Adjacent sequences: A274448 A274449 A274450 * A274452 A274453 A274454

Keyword

nonn

Author

Jeffrey Shallit, Jun 23 2016

Extensions

a(19)-a(32) from Bjarki Ágúst Guðmundsson, Jul 07 2016

Status

approved