Let's assume that each couple of rabbits give birth to two baby rabbits.
Let's count the number of couple of rabbits. At the beginning, we've 1 couple of young rabbit
F_1 = 1
Next year, they'll be adult rabbits, but won't have children yet :
F_2 = 1
On the third year, they'll a two baby rabbits, that is one couple
F_3 = 2
On the forth year, the first parent will have two baby rabbits again, but young rabbits won't be old enough to do so
F_3 = 2 + 1 = 3
On the fifth year, we've got two couples that can have little rabbits and one that cannot :
F_3 = 3 + 2 = 5
and so on... Each year, the number of couple is :
- the number of rabbits that lived the year before, that is F_{n-1}
- plus the number of rabbits that were born that year, that is the number of couple old enough to proceate, that is F_{n-2}
To conclude :
F_n = F_{n-1} - F{n-2}
Funny, isn't it ? Ok, that is not very realistic and very accurante, but who cares ? ;)
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