$$\eqalign{
x_n &= (n+1)^2 +(n+2)^2 + [(n + 1)(n + 2)]^2 \cr x_n &= n^2 + 2n +
1 +n^2 + 4n + 4  + [n^2 + 3n + 2]^2 \cr
 &= n^4 + 6n^3 + 15n^2 + 18n + 9 \cr
&= [n^2 + 3n + 3]^2 \cr } $$
\end
