A275061 Number of binary strings of length n avoiding 4-antipowers.

1, 2, 4, 8, 16, 32, 64, 128, 232, 432, 808, 1512, 1644, 2258, 3228, 5034, 3648, 4170, 5166, 6780, 4484, 5136, 5874, 7484, 6520, 8438, 10858, 13134, 11396, 13366, 17008, 20690, 20142, 22822, 27448, 33384, 34314, 37118, 41442, 47272, 50132, 54950, 60632, 67572, 71028, 78086, 85828, 92608, 95542, 102182, 112008

Offset

0,2

Comments

A 4-antipower is 4 consecutive blocks, no two of which are the same, like (11)(10)(01)(00). By "avoid" we mean the binary string has no contiguous block within it that is a 4-antipower.

Links

Table of n, a(n) for n=0..50.

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

Lukas Fleischer, Samin Riasat, Jeffrey Shallit, New Bounds on Antipowers in Binary Words, arXiv:1912.08147 [cs.FL], 2019.

Crossrefs

Sequence in context: A297526 A229617 A306316 * A230177 A216264 A054045

Adjacent sequences: A275058 A275059 A275060 * A275062 A275063 A275064

Keyword

nonn

Author

Jeffrey Shallit, Jul 15 2016

Status

approved