Given recurrence relation $(a_{n+1})^2 = a_n - (a_{n-1})^2$ and $a_0 = 0, a_1 = 1$
How do you solve this? I have discussed this with some of my collegues, but find no steps. Suggesting about generating function seem effective though, but there are square of sequence, and we don't know how to make it.
If $(a_n) $ is a real sequence, then such a sequence does not exist:
In the first step we get $a_2= \pm 1$. Then:
$a_3^2=a_2-1$. This gives $a_2=1$. Hence $a_3=0$. But then we get $a_4^2=-1$, a contradiction.