Statistics of lattice animals (polyominoes) and polygons

We have developed an improved algorithm that allows us to enumerate the number of site animals (polyominoes) on the square lattice up to size 46. Analysis of the resulting series yields an improved estimate, τ = 4.062 570(8), for the growth constant of lattice animals and confirms, to a very high degree of certainty, that the generating function has a logarithmic divergence. We prove the bound τ > 3.903 18. We also calculate the radius of gyration of both lattice animals and polygons enumerated by area. The analysis of the radius of gyration series yields the estimate v = 0.641 15(5), for both animals and polygons enumerated by area. The mean perimeter of polygons of area n is also calculated. A number of new amplitude estimates are given.