Answer to Question #302219 in Combinatorics | Number Theory for salomo

Question

Qn 2. You are putting a strip of tiles on a wall. The strip consists of two

columns of n tiles each.

n = 6

You have three different colours with which to paint the tiles. You want to

colour the strip in such a way that each tile has a uniform colour and that

the colour of a given tile is different from the colour of the tile next to it in

the same row and from the colour of the tile above it or below it in the same

column.

Find a formula, depending on n, for the number of colourings that satisfy

the given constraints.