Is this solvable-

$D(n+1)=21\left(\frac{M-\frac{3}{32}Tn\sum_{i=0}^{n}\frac{D(i)+18}{22}-A}{\left( \frac{(2n^2-14n+47)n}{64}+1\right)\frac{3}{5}T+\left(\frac{-2n^2+14n+17}{64} \right )Tn} -1 \right ) +3$

where D(0)=0

This is an expression I came up with while trying to solve another problem in physics (time taken by a system to reach a threshold which is dependent on other systems which have already reached the threshold). Here M, T and A are all constant parameters of the system. I am planning to solve this numerically but I was wondering if there actually is a way to reduce this expression (have D only on one side).

I don't have a lot of background in solving recursions except what I learnt in one course back when, and I don't think we ever learnt how to do something like this. Any help is appreciated


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