Suppose that you have an assortment of lego blocks, they're all height 1 and width 1 but can have varying lengths. The lengths of the blocks will be an input of the program and you have an infinite number of each block length. (So available_block_lengths = []int)

You want to build a wall of length X and height H, in such a way that the intersection of two blocks in one layer never lines up with the intersection of two blocks in a different layer. Given this information, output the number of different valid permutations in which such a wall can be built with the available blocks.

So for example, if we had blocks of length 1 and 2 and the wall width was 3 and height 3, the output should be 2:

|oo|o|
|o|oo|
|oo|o|

And

|o|oo|
|oo|o|
|o|oo|