Whittington–Soteros asymptotic conjecture for polyominoes

Let $P(n)$ denote the number of polyominoes with $n$ cells, and let

$$\lambda=\lim_{n\to\infty}\sqrt[n]{P(n)}$$

be Klarner's constant. Whittington–Soteros conjecture. There exist constants $A,T$ such that

$$P(n)\sim A n^{-T}\lambda^n.$$

This is a widely believed estimate for the number of polyominoes and predicts the polynomial correction to the exponential growth $\lambda^n$; the paper proves only a weaker lower bound with a factor of the form $n^{-T\log n}$.