8. A sequence is defined recursively: $$ a_{1}=1, a_{2}=4, a_{3}=9, a_{n}=a_{n-1}-a_{n-2}+a_{n-3}+2(2 n-3) \text { for } n \geq 4 $$ Find $$ \begin{array}{1} a_{4}= a_{5}= a_{6= \end{array} $$ Based on specific terms suggest a formula for $a_{n}$ $$ a_{n}= $$ Use strong induction to prove that your formula is correct. Basic cases: Inductive Hypothesis: Inductive step: CS.VS. 1121||