A Single Pair of Rabbits (Male and Female) Is Born $s _ { n } =$

Essay

A single pair of rabbits (male and female) is born at the beginning of a year. Assume the following conditions: (a) Rabbit pairs are not fertile during their first two months of life, but thereafter they give birth to four new male/female pairs at the end of every month; (b) No deaths occur. Let $s _ { n } =$ the number of pairs of rabbits alive at the end of month $n$ , for each integer $n \geq 1$ , and let $s _ { 0 } = 1$ . Find a recurrence relation for $s _ { 0 } , s _ { 1 } , s _ { 2 } , \ldots$ Justify your answer carefully.