Kolmogorov Complexity, struggle with equation
The statement is equivalent to \begin{align}n+1=\log_2\left(\frac{|(01)^{2^n}|}2\right)&amp;\impliedby |(01)^{2^n}|=2^{n+2}.\end{align} If $(01)^{2^n}$ means $\underbrace{(01)(01)(01)\cdots(01)}_{2^n\,\text{times}}$ then the statement is incorrect as $|(01)^{2^n}|=2^{n+1}$ as you have correctly obtained.