Fibonacci Rabbits

generations

4

show

labels

rabbits

nm[m[m,n],n[m]],Textgenerations,{-2,3.10473},Textnumber of pairs,{3.77413,3.10473},{Text[1,{-2,2.6612}],Text[2,{-2,1.77413}],Text[3,{-2,0.887066}],Text[4,{-2,0.}]},{Text[1,{3.77413,2.6612}],Text[1,{3.77413,1.77413}],Text[2,{3.77413,0.887066}],Text[3,{3.77413,0.}]}

a pair of rabbits:born|mature|survive

In 1202 Fibonacci investigated how fast rabbits could breed.

Suppose a pair of rabbits, one male and one female, start a family. Rabbits mature at the age of one month (labeled "m") and a female produces a new pair of rabbits (labeled "n") at the end of its second month.

Suppose that the rabbits survive forever and that a female always produces one new pair (one male, one female) every month, giving the original pair and a new one.

How many pairs will there be in eight generations?