In Problems 58-60, further assume that young rabbits become adults after two months and produce another pair of offspring at that time. A rabbit breeder begins with one adult pair. Let \(a_{n}\) denote the number of adult pairs of rabbits in this "colony" at the end of \(n\) months.

Explain why \(a_{1}=1, a_{2}=1, a_{3}=2, a_{4}=3\), and, in general, \[a_{n+1}=a_{n-1}+a_{n}\]
for \(n=2,3,4, \cdots\)