Recurrences seem lovely!

Probability Level 4

A sequence starts with a0=0a_0=0 and the next term is a1=1a_1=1.

If the further terms are given by

an=7an110an2+7\displaystyle a_n= 7a_{n-1}- 10a_{n-2} + 7

Then find the last 3 digits of a20a_{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 is bit easier than this one.

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