For every integer
![n \geq 2](/media/m/2/1/f/21fe2458de6d1580c44fd06e0fac11bb.png)
determine the minimum value that the sum
![\sum^n_{i=0} a_i](/media/m/1/2/0/1200245ba00b4ab9377d17246f63d0ca.png)
can take for nonnegative numbers
![a_0, a_1, \ldots, a_n](/media/m/4/5/a/45a875189a0ae4e5fbc7fd19c6ea5da3.png)
satisfying the condition
![a_i \leq a_{i+1} + a_{i+2}](/media/m/1/f/e/1fe38c3b12d040ad884e4f0276f4b769.png)
for
%V0
For every integer $n \geq 2$ determine the minimum value that the sum $\sum^n_{i=0} a_i$ can take for nonnegative numbers $a_0, a_1, \ldots, a_n$ satisfying the condition $a_0 = 1,$ $a_i \leq a_{i+1} + a_{i+2}$ for $i = 0, \ldots, n - 2.$