Hi we all know famous Rabbit breeding Fibonacci sequence. If you don't here is a brief explanation:
You can solve Fibonacci’s problem simply by keeping a count of the rabbits at each month during the year. At the beginning of January, there are no rabbits, since the first pair is introduced sometime in that month, which leaves one pair of rabbits on February 1. Since the initial pair of rabbits is newborn, they are not yet fertile in February, which means that the only rabbits on March 1 are the original pair of rabbits. In March, however, the original pair is now of reproductive age, which means that a new pair of rabbits is born. The new pair increases the colony’s population—counting by pairs—to two on April 1. In April, the original pair goes right on reproducing, but the rabbits born in March are as yet too young. Thus, there are three pairs of rabbits at the beginning of May. From here on, with more and more rabbits becoming fertile each month, the rabbit population begins to grow more quickly.
Can you help me answer the following question?
Modify Fibonacci’s rabbit problem by introducing the additional rule that rabbit pairs stop reproducing after giving birth to three litters. How does this assumption change the recurrence relation? What changes do you need to make in the simple cases?
Tha above question from Computer Science but recursion is same in math and computer science.