Use of model solutions in random sequential adsorption on a lattice

We consider random sequential adsorption on a lattice. We use analytical results on the Bethe lattice and cactus as references to develop systematic perturbationlike expansions which are very rapidly convergent. The latter produces the jamming density of a square lattice with an accuracy within ${10}^{\mathrm{-}5}$. This expansion is based on both physical and mathematical considerations and is not restricted to random sequential adsorption.