Eccoci.

A $30 \times 30$ grid of squares contains $900$ fleas, initially one flea per square.
When a bell is rung, each flea jumps to an adjacent square at random (usually $4$ possibilities, except for fleas on the edge of the grid or at the corners).

What is the expected number of unoccupied squares after $50$ rings of the bell? Give your answer rounded to six decimal places.