题目213：跳蚤

欧拉计划

Flea Circus

A 30×30 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.

题目：

一个 30×30 格的网格里有 900 只跳蚤，一开始，一只跳蚤一个方格。

当钟声响起，跳蚤们就随机地跳到相邻的方格上（一般有四个可能，除了在角落的或在网格最边上的跳蚤们）。

请问，钟声响了 50 次后，空方格的期望数目是多少？给出答案，精确到小数点后六位。