# Changing the index variable in a recursion relation

Can I change $$x_{n+2} = 14x_{n+1} - 49x_n + n7^n\\ n>=0\\ x_0 = 1\\ x_2=14$$ to $$x_{n} = 14x_{n-1} - 49x_{n-2} + n7^n\\ n>=2\\ x_0 = 1\\ x_2=14$$

And it's same? I need to find solutions of recursive equations, but have no idea how do it when have $$x_{n+2} =...$$ not $$a_n =...$$ like in others exercise.

Yes, you can do it but notice that when you changes $$x_n$$ to $$x_{n-2}$$ in the second term you should have done the same to $$n\cdot 7^n$$ so the recursion looks like $$x_n=14x_{n-1}-49x_{n-2}+(n-2)\cdot 7^{n-2}.$$