Mortal Fibonacci Rabbits

Wabbit Season

In “Rabbits and Recurrence Relations”, we mentioned the disaster caused by introducing European rabbits into Australia. By the turn of the 20th Century, the situation was so out of control that the creatures could not be killed fast enough to slow their spread.
The conclusion? Build a fence! The fence, intended to preserve the sanctity of Western Australia, was completed in 1907 after undergoing revisions to push it back as the bunnies pushed their frontier ever westward. If it sounds like a crazy plan, the Australians at the time seem to have concurred.
By 1950, Australian rabbits numbered 600 million, causing the government to decide to release a virus (called myxoma) into the wild, which cut down the rabbits until they acquired resistance. In a final Hollywood twist, another experimental rabbit virus escaped in 1991, and some resistance has already been observed.
The bunnies will not be stopped, but they don’t live forever, and so in this problem, our aim is to expand Fibonacci’s rabbit population model to allow for mortal rabbits.


Recall the definition of the Fibonacci numbers from “Rabbits and Recurrence Relations”, which followed the recurrence relation


and assumed that each pair of rabbits reaches maturity in one month and produces a single pair of offspring (one male, one female) each subsequent month.

Our aim is to somehow modify this recurrence relation to achieve a dynamic programming solution in the case that all rabbits die out after a fixed number of months.


Positive integers n ≤ 100 and m ≤ 20.


The total number of pairs of rabbits that will remain after the n-th month if all rabbits live for m months.


Change n and m with the values given in the dataset:

n = 89 #replace input                                                                        
m = 16 #replace input                                                                       
bunnies = [1, 1]                                                               
months = 2
count = []                                                                     
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)                          
        bunnies.append(bunnies[-2] + bunnies[-1] - bunnies[-(                  
            m + 1)])                                                           
    months += 1                                                                
Important note:

This problem is taken from Please visit ROSALIND to find out more about Bioinformatics problems. You may also clink onto links for the definitions of each terminology.