Mortal Fibonacci Rabbits

In this Rosalind problem we are revisiting the Fibonacci Rabbits. This time the bunnies sadly aren't immortal and will die after m months. Apart from that they behave as in the previous problem but they only produce one pair of offspring per month in adulthood. This leaves us with two different recurrence relations to calculate the amounts of rabbits present in any given month n. The months before any rabbits start dying off, i.e. when n ≤ m can be described by the recurrence relation of the Fibonacci numbers. The months after this, i.e. when n > m, can be described by the following formula:

Fn = Fn-1 + Fn-2 - Fn-(m+1)

To calculate the number of rabbits after 96 months, when the rabbits are dying after 17 months, I wrote the following program:

n = 96                                                                         

m = 17                                                                         

bunnies = [1, 1]                                                               

months = 2                                                                     

while months < n:                                                              

    if months < m:                                                             

        bunnies.append(bunnies[-2] + bunnies[-1])                              

    elif months == m or count == m + 1:                                        

        bunnies.append(bunnies[-2] + bunnies[-1] - 1)                          

    else:                                                                      

        bunnies.append(bunnies[-2] + bunnies[-1] - bunnies[-(                  

            m + 1)])                                                           

    months += 1                                                                

print(bunnies[-1])                                                             

So, care to take a guess what the result after 96 months was? 51159459138167757395. Pairs...