On two-variable recurrence sequences with a tiling application

In discrete mathematics, recursive systems of equations occur frequently. For this reason, in this article we focus specifically on a special case of these: a type of nested two-variable recursive systems. We develop a method by which these systems can be transformed into equivalent recursive relations containing a single sequence. As an application, we analyze a tiling problem arising on a 2 × n grid and derive the corresponding recursive relation. The example illustrates the efficiency and simplicity of the proposed method.