Recurrences part 3

$\displaystyle a_n= 7a_{n-1}- 10a_{n-2}+ 3^n$

Consider the above sequence, with initial conditions $$a_0=0$$ and $$a_1=1$$.

Find the last 3 digits of $$a_{20}$$.

Details and Assumptions

If you don't know how to get the solutions for recurrence relations, you may try to learn it here.

This note will prove helpful in the coming problems of this series.

First Problem and Second problem are easier than this one

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