A floor tiling company wants to tile a hallway that is n feet long and 3 feet wide; unfortunately, they only have tiles that are 1 foot by 3 feet in length.(a) Find a recurrance for F(n), the number of ways the floor tilers can completely tile an n by 3 hallway. Provide base cases as needed for your recurrance, but do not solve the recurrance.(b) Use this recurrance to demonstrate that F(n) lt;= (3/2)^n for all n gt;= 1.
let the first slot be filled with a tile covering the whole breadth. then the remaining slots can be filled in f(n-1) ways. again if the first slot be covered in 1ft /3ft way then the remaining slots may be filled in f(n-3) ways. so in my opinion f(n)=f(n-1)+f(n-3)
