Question 26
(ITA) For every integer $n\ge2$ determine the minimum value that the sum $a_0+a_1+\cdots+a_n$ can take for nonnegative numbers $a_0,a_1,\ldots,a_n$ satisfying the condition
$$a_0=1,\quad a_i\le a_{i+1}+a_{i+2}\quad\text{for }i=0,\ldots,n-2.$$
$$a_0=1,\quad a_i\le a_{i+1}+a_{i+2}\quad\text{for }i=0,\ldots,n-2.$$