No-free-ends method for lattice animals and vertex models with arbitrary number of states

A new no-free-ends method for generating power series expansions for vertex models with arbitrary number of states is described. It is based on first-order differential equations providing a recurrent relation connecting the free-ends part of the series expansion in the (n + 1)th order with the nth and (n - 1)th order of the complete expansion. The number of necessary no-free-ends graphs can be further reduced for symmetric systems by eliminating the nodes which have two neighbors and their incident bonds are in different states.