  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.
