Consider the following adaptation of the example of Rabbits on an island. A pair of rabbits on an island does not breed until they are 2 months old. After they are 2 months old, each pair of rabbits produces two pairs (instead of one pair) each month. Find a recurrence relation for fn, the number of pairs of rabbits on the island after n months, assuming that no rabbits ever die. It is enough to write the recurrence relation for fn and the initial conditions. What are the degree and the characteristic equation of the recurrence relation an = an-1- 6an-3? Suppose that the roots of the characteristic equation of a linear homogeneous recurrence relation are -2, -2, -2 and 3. What is the form of the general solution?

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