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**Henderson** Thank you- that is the path I have taken, and finding the roots using the characteristic equation has been something we have practiced in class. I had found the roots of $\displaystyle 1+i$ and $\displaystyle 1-i$, and the coefficients of $\displaystyle c_{1} = c_{2} = 1$, but stopped there, because when I check my working up to that point, I get different values than the sequence gives me.

For example, when $\displaystyle n=7$:

$\displaystyle u_{7} = 176$

The sequence I've made to get there is

$\displaystyle u_{n}$:$\displaystyle (2, 2, 0, 4, -8, 24, -64, 176)$

But $\displaystyle 1 (1 + i) ^7 + 1 (1 - i) ^7$

$\displaystyle = (8 - 8i) + (8 + 8i)$

$\displaystyle =16 $

Any thoughts?