Here is how you would set up the recurrence:
To layout a garden with 10n cm, we can use any 2 of the 10 cm blocks, and layout the rest of the 10(n-1) cm.
Or we can use any 3 of the 20 cm blocks, and layout the rest of the 10(n-2) cm.
Hi, I have a problem with below exercise:
Express the solution to each of the following counting problems in terms of a difference equation, then use a generating function to solve the difference equation to give an explicit solution.
I am making a border for the front of a garden bed out of small bricks that are 10 cm long and larger bricks that are 20 cm long. If the small bricks come in two colours, and the larger bricks come in three possible colours, how many different borders of length 10n cm can I make?
Thanks in advance
Sure. Multiply the recurrence by , then do a summation.
Also, this may help: http://brooks-pdx.pbworks.com/f/CS340-Section5.4.pdf