Fibonacci

This problem was studied by Leonardo Fibonacci in the thirteenth century. The numbers of rabbits form the Fibonacci series. This series has important applications in several problems that have nothing to do with rabbits. Call the Nth number in the series fib(N):

Here is the rule for filling the chart, rewritten for fib(N):

fib( N ) = fib( N-1 ) + fib( N-2 )

Look at the chart to verify that the rule works.