The cylindrical contact homology of universally tight sutured contact solid tori

We calculate the sutured version of cylindrical contact homology of a sutured contact solid torus $(S^1\times D^2,\mathrm{\Gamma },\xi )$, where $\mathrm{\Gamma }$ consists of $2n$ parallel sutures of arbitrary slope and $\xi$ is a universally tight contact structure. In particular, we show that it is non-zero. This computation is one of the first computations of the sutured version of cylindrical contact homology and does not follow from computations in the closed case.