Fibonacci Sequences Question

Question

two new male/female pairs of rabbits at the age of 1 month and six new male/female pairs of rabbits at the age of 2 months and every month afterward. Assume that there is only one male/female pair of rabbits at the beginning of a year. Further assume that no rabbits die in the farm. Let a(n) be the number of male/female pair of rabbits in the farm at the end of month n.
find recurrence relation
I got this one -> a(n)=a(n-1)+6a(n-3)+2[a(n-2) - a(n-3) ]

simplify          -> a(n)=a(n-1)+2a(n-2)+4a(n-3)

how to turn above relation to a(n)=a(n-1)+?*a(n-2)

Answer 1

From

a(n)=a(n-1)+2a(n-2)+4a(n-3)

The next line would be achieved by converting the (n - 3) into (n - 1) or (n - 2) terms.