Ground states of Nicolai and mathbb{Z}₂ Nicolai models

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.