Relation between multiples of recurrences

23 Views Asked by At

If I have a recurrence

$$R_n = aR_{n-1}+bR_{n-2}, R_1 = x, R_2 = y$$

and now I want to consider this new recurrence

$$Q_n = c(aQ_{n-1}+bQ_{n-2})$$

Is there any way to relate the two (perhaps by setting some specific initial values of $Q$)?