近几年在各级各类考试中经常出现这类试题 :在给定的几个区域中栽种植物 ,要求在相邻的区域中栽种不同的植物 ,求共有多少不同的栽种方法 .这类问题实际上是一类染色问题 (或地图着色问题 ) .本文试图将这类问题归结为求一类递推数列的通项公式 ,并给出这类问题的一般计数方法 In recent years, such questions have frequently appeared in examinations of all types and at all levels: planting plants in a given number of areas requires the planting of different plants in adjacent areas, and asking how many different planting methods there are in common. In fact, it is a kind of dyeing problem (or map coloring problem). This paper attempts to reduce this type of problem to a general term for a class of recursive sequences, and gives a general counting method for such problems.