85. Bacteria have the following development rule: each one lives for 1 hour and every half hour it produces one new one (a total of two during its life). What will be the offspring of one bacterium 6 hours after its birth?
85. Let's call bacteria "young" if their age does not exceed half an hour, and "old" if they have lived for more than half an hour. Let's take half an hour as the unit of time. Denote the number of bacteria at moment $n$ by $u_{n}$. At moment $n-1$, $u_{n-1}$ bacteria are born, so by moment $n$ there are $u_{n-1}$ young bacteria, each of which produces one new bacterium, and $u_{n}-u_{n-1}$ old bacteria, each of which also reproduces. Therefore, by moment $n+1$, the number of bacteria is $u_{n-1}+u_{n-1}+u_{n}-u_{n-1}$, i.e.,

$$
u_{n+1}=u_{n}+u_{n-1}
$$

Given that $u_{1}=1, u_{2}=2$. The required number of bacteria is (*) shows that $u_{13}=377$.

The sequence $u_{n}$ coincides with the Fibonacci sequence (see N. N. Vorobiev, Fibonacci Numbers, 3rd ed., "Nauka", 1969$)$