Given a_0 = 1 and a_1 = 5 and the general relation a_n^2 - a_{n + 1} = (-1)^n for n >= 1 find a_3
This is true: a2n−an+1=(−1)n
And we have a1=5
So this must be true: 52−a2=(−1)1, or 26=a2.
Similar logic:
262−a3=(−1)2
a3=675
+309 
