Если не ошибаюсь, в задаче Фибоначчи нет ограничения на `k', т.е. в той идеальной модели кролики живут бесконечно.
Цитата из http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html:
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Fibonacci's Rabbits
The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances.
Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was...
How many pairs will there be in one year? »
З.Ы. Думаю, что эта задача тоже на комбинаторику, но более сложная. Я не знаю как её решить, но полагаю следует думать.
