In = an+3 + (a+1)2n+3 , when n=-1 and n=0 it can be shown that it is divisible by a2+a+1
In+1 = an+4 + (a+1)2n+5
In+1 - In = (an+4 - an+3) + [(a+1)2n+5 - (a+1)2n+3]
which can be ultimately reduce to In+1 = a.In + (a2+a+1).(a+1)2n+3
So, by induction method u can prove. Not true for n less than -1.