# Find a recurrence word problem.

1. Jun 18, 2012

### charmedbeauty

find a recurrence,,, word problem.

1. The problem statement, all variables and given/known data

A rectangular board 2cm wide and ncm long is to be covered with smaller tiles of size 2cmx2cm and 1cmx2cm. There is an unlimited supply of both types of tile.

For each n=1,2,... let an be the number of ways that a board of length n cm can be covered with the two types of tile.

a) find a recurrence relation for an , n>2.

b) find a5

2. Relevant equations

3. The attempt at a solution

a) im not really sure how these answers are meant to be set out... its something like an= an-1...

I imagine when n=3, there is a 2x3 board so it can be tiled with with 3(1x2) or 1(2x2)+1(1x2) tiles. so it can be done in two ways?

n=4 .... 2(2x2) or 4(1x2) or 1(2x2)+ 2(1x2) so 3 ways

n=5... 2(2x5)+1(1x2) or 1(2x2)+3(2x1) or 5(1x2) so 3 ways.

n=6 .... 3(2x2) or 2(2x2) +2(1x2) or 1(2x2) +4(1x2) or 6(1x2) so 4 ways.

am I meant to be seeing a pattern? maybe an is the same for (2n) and (2n+1)

all I can think of is that a 2cmx2cm = 2 (1cmx2cm) tiles.

I imagine that part b) has to do with part a) so I can't solve without a.

any help greatly appreciated.

Thanks

Last edited: Jun 18, 2012