"Start with a pair of rabbits, (one male and one female) born on January 1. Assume that all months are of equal length and that :
1. rabbits begin to produce young two months after their own birth;
2. after reaching the age of two months, each pair produces a mixed pair, (one male, one female), and then another mixed pair each month thereafter; and
3. no rabbit dies.
How many pairs of rabbits will there be after one year?"
Fibonacci's Solution: The Fibonacci Sequence!
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
So, at the end of the year, there will be 144 pairs of rabbits, all resulting from the one original pair born on January 1 of that year.
Keep the assumptions of rabbit reproduction the same as for the Fibonacci numbers, but with one change. Now assume that the time to fertility for a newborn is 2 months rather than 1. Starting with a newborn male and female, make a table which gives the number of pairs of rabbits after each month for 10 months. What is the mathematical relationship that gives the terms of this sequence of numbers?