login
Number of length-n overlap-free binary words that are squares.
0

%I #24 Jan 05 2024 00:14:39

%S 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,

%T 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,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

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

%F 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.

%e 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.

%Y Cf. A007777.

%K nonn,easy

%O 1,2

%A _Jeffrey Shallit_, Jan 04 2024