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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