  We derive explicit recursions for the ground state generating functions of
the one-dimensional Nicolai model and $\mathbb{Z}_2$ Nicolai model. Both are
examples of lattice models with $\mathcal{N}=2$ supersymmetry. The relations
that we obtain for the $\mathbb{Z}_2$ model were numerically predicted by
Sannomiya, Katsura, and Nakayama.
