A368707 Number of length-n overlap-free binary words that are squares.

0, 2, 0, 2, 0, 6, 0, 4, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Links

Table of n, a(n) for n=1..86.

Formula

a(2) = 2; a(2^n) = 2^{n-1} for n>=2; a(3*2^n) = 3*2^n for n>=1; a(n) = 0 for all other entries.

Example

The overlap-free words of length 6 are  001001, 010010, 011011, 001011, 001100, 001101, 010011, 010110, 011001, 011010, and their binary complements, but only the first 3 are squares.

Crossrefs

Cf. A007777.

Sequence in context: A002117 A042970 A158327 * A136581 A364558 A364559

Adjacent sequences: A368704 A368705 A368706 * A368708 A368709 A368710

Keyword

nonn,easy

Author

Jeffrey Shallit, Jan 04 2024

Status

approved