  We express the coverage (occupation fraction) $\theta$, in powers of time $t$
for four models of two-dimensional lattice random sequential adsorption (RSA)
to very high orders by improving an algorithm developed by the present authors
[J. Phys. A 29, L177 (1996)]. Each of these series is, to the best of our
knowledge, the longest at the present. We analyze the series and deduce
accurate estimates for the jamming coverage of the models.
