the system.

A sketch of the used Cayley tree terminated after the 4-th generation step is shown in Fig. \[Fig1\]a. This Cayley tree is embedded into the lattice that consists of a sea of Cayley trees connected to each other through their termination sites. The present theory, initially developed for homogeneous polymers, relies on establishing a connection between the local configuration of species occupying lattice sites of the Cayley tree and an average local field entering into the grand partition function (GPF) of the system. This relation is derived by choosing the local configuration weights according to a certain field relation between internal and external interactions in the neighborhood of the central site of the Cayley tree. For the considered case of the layered structure in the presence of adsorbing surface, this relation and resulting GPF must be separately determined for each layer of the system. In order to construct a layered structure in the proposed formalism, we embed the Cayley tree into 3 consecutive layers as shown in Fig. 1b. Finally, the equal probability condition [@Roberts; @Chang1939] of the site occupation on the Cayley tree is applied to that particular structure. Using the recursive relations between consecutive layers makes 