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Jovian hares are hermaphrodite. Each mature Jovian hare produces one leveret during each breeding cycle. Each leveret takes two breeding cycles to mature into a fully-grown hare, and then lives for ever. Starting with a single newly-born Jovian leveret,how many hares (including leverets) are there after 47 breeding cycles?

This is the question that I am being asked to consider. I have found the equation to calculate the number of hares and leverets after $n$ breeding cycles. It is $M_n = M_{n-1}+M_{n-3}$ and have found the number of hares and leverets that will present after 47 breeding cycles. I am just a little iffy on how to write a proof of the recurrence relation. Can someone enlighten me on how to do this for this problem?

Dylan
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1 Answers1

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How many hares are there after $n$ cycles?

  • All the hares that were alive last cycle, because they live forever. This is $M_{n-1}$ hares.

  • One leveret for each fully-grown hare; that is, one for each hare that is at least three cycles old. This is $M_{n-3}$ hares.

Matthew Leingang
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