# Recursions in Recursions - 2

Algebra Level 4

$\large { \begin{eqnarray} a_{n} & =& 2a_{n-1} + 3 \\ b_{n} &=& b_{n-1} + b_{n-2} \\ \end{eqnarray} }$

For natural number $$n$$, consider the two recurrence relation above subjected to conditions, with $$a_1 = 0, b_{1} = b_{2} = 1$$.

If the value of expression $$(a_{b_{2015}} + 3)(a_{b_{2016}} + 3)$$ can be expressed as $$p^{b_{q}} \dfrac{r}{s}$$, where $$b_{q}$$ is one of the term in the recurrence relations sequence above and $$p, r$$ and $$r, s$$ are pairwise coprime integers.

Find the value of $$(p+q+r+s) \bmod {673}$$.

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