The recurrence relation is solvable to $\displaystyle a_n=\tfrac{c}{2}n(n-1)+2(1-n)(n-1)$ for some constant $\displaystyle c$. Do you see how?
Hey
I have not done this method
but I solved the question by progressions and some logic later on to arrive at answer. My answer is coming out 249. and I know my method is not appropriate can you deduce the answer by recurrence relation