Question 120
Let the sequence $\left(a_{n}\right)_{n \geqslant 1}$ be defined by $a_{1}=3, a_{2}=11$ and $a_{n}=4 a_{n-1}-a_{n-2}$ for $n \geqslant 3$. Prove that every term of this sequence is of the form $a^{2}+2 b^{2}$ for some natural numbers $a$ and $b$.
(Đorđe Baralić)
(Đorđe Baralić)