this one easier

Question

After a lifetime of hard work, one of your friends was able to buy a plot of land for himself and build a portable villa on it. The work went well and reached the tiling stage.
Now he asks you to help him as an expert programmer.
There are two types of tiles on the market, either square or rectangular. Rectangles can also be used horizontally or vertically. The square has no other use!
The square tiles are 2 * 2. Rectangular tiles 1 * 3.
Suppose the ground is K * N, where K can be 1 to 3 and N between 1 to 10,000.
You should use these tiles to cover the entire floor, so that all the floor cells are covered exactly by one tile.
The output is the total number of possible paths.

Entrance:
2
5
Output:
7

Answer 1

I don't see how they got 7 when input is 2 * 5.
Patterns for 2*5:
Sq.RR

RR.Sq

Can't use half a tile, can't use a 1*3 sideways. Combinations is 2.
If they want permutations instead of combinations then the answer is 4.

Am I interpreting the question wrong?

Answer 2

your Try??