Recurrences part 4

A sequence starts with $a_0=0$ and $a_1=1$ .

If the further terms are given by

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

Then find the last 3 digits of $a_{20}$ .

Details :- 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 , Second problem and Third Problem are easier than this one.