Checkmate (aka the urinal problem)

Oasis, 5 bytes

Code

cd+2V

Extended version

cd+211

Explanation

1 = a(0)
1 = a(1)
2 = a(2)

a(n) = cd+
       c      # Calculate a(n - 2)
        d     # Calculate a(n - 3)
         +    # Add them up

Try it online!

int g(int u){return u>1?g(u-2)+g(u-3):1;}

The sequence just adds previous elements to get new ones. Hat tip to orlp and Rod for this shorter method ;)

Old:

int f(int u){return u<6?new int[]{1,1,2,2,3,4}[u]:f(u-1)+f(u-5);}

After the fifth element, the gap in the sequence rises by the element five previous.

f=lambda n:n>1and f(n-2)+f(n-3)or 1

Generating the actual sets:

lambda n:["{:0{}b}".format(i,n).replace("0","-").replace("1","X")for i in range(2**n)if"11"not in"{:0{}b}".format(i*2,2+n).replace("000","11")]