Enumerations of lattice animals and trees

We have developed an improved algorithm that allows us to enumerate the num ber of site animals on the square lattice LIP to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of bo th lattice animals and trees up to size 42. Analysis of the resulting serie s yields an improved estimate, lambda =4.062570(8), for the growth constant of lattice animals, and, lambda (0)=3.795254(8), for the growth constant o f trees, and confirms to a very high degree of certainty that both the anim al and tree generating Functions have a logarithmic divergence. Analysis of the radius of gyration series yields the estimate, nu =0.64115(5), for the size exponent.