We introduce a natural generalization of Maya diagrams -- the space of infinite Fibonacci configurations, which are specified functions on $\mathbb{Z}$ with values $1$ and $0$. Infinite Fibonacci configurations are particularly interesting as soon as they parametrize Feigin-Stoyanovsky type bases in lattice vertex superalgebras $V_{\sqrt{N}\mathbb{Z}}$ and their irreducible modules. We calculate the character of such configurations space by two different ways and obtain series of combinatorial identities. These identities turn out to be Durfee rectangle identities with shifts in base and height.