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Population explosion in a rabbit farm

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You own a rabbit far. Every week each pair of rabbits has two baby rabbits. However, the baby rabbits first reproduce when they are two weeks old. Initially you have a pair of newborn rabbits. How many pairs you have after n weeks?

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The solution shows how to get a general solution from some initial calculations.

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Though not stated specifically in the question these conditions must be met in order to get a meaningful solution:

1. Rabbits never die
2. A rabbit reaches reproductive maturity exactly two weeks after birth, that is at the beginning of its third week of life
3. Rabbits are always born in male-female pairs. At the beginning of ...

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