Recursive Sequence

A sequence $$\{ a_i\}$$is defined by the recurrence relation $$a_{n} = 40 - 4a_{n-1}$$ with $$\ a_0 = -4$$. There exists real valued constants $$r, s$$ and $$t$$ such that $$a_i = r \cdot s^i + t$$ for all non-negative integers $$i$$. Determine $$r^2+s^2+t^2$$.

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