# Recurrence Relation jumping forward and backwards between bounds of 0 and m

Question

What I have gotten so far is as follows: $$q_{m,k} = q_{m,k-1}a_{n-1}$$ for $$2|k$$, otherwise it is $$q_{m,k} = q_{m,k-1} (m - a_{k-1})$$ Is there any way to make this into one recurrence relation and eliminate $$a_i$$ from the equation?

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