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

Author

Jeffrey Shallit, Jan 04 2024

Keywords

• nonn
• easy

Examples

			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.

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.