Example(fibonacci sequence): 13世纪初意大利数学家 fibonacci研究过著名的兔 子繁殖数目问题 A young pair rabbits (one of each sex) is placed in enclosure. A pair rabbits dose not breed until they are 2 months old, each pair of rabbits produces another pair each month. Find a recurrence relation for the number of pairs of rabbits in the enclosure after n months, assuming that no rabbits ever die Solution: Let fn be the number of pairs of rabbits after n months ()Born during month n (2)Present in month n-1 Fn=Fn+Fn-, FI=F2=1▪ Example(Fibonacci sequence): ▪ 13 世纪初意大利数学家 Fibonacci 研究过著名的兔 子繁殖数目问题 ▪ A young pair rabbits (one of each sex) is placed in enclosure. A pair rabbits dose not breed until they are 2 months old, each pair of rabbits produces another pair each month. Find a recurrence relation for the number of pairs of rabbits in the enclosure after n months, assuming that no rabbits ever die. ▪ Solution: Let Fn be the number of pairs of rabbits after n months, ▪ (1)Born during month n ▪ (2)Present in month n-1 ▪ Fn=Fn-2+Fn-1，F1=F2=1