How many cubic bipartite graphs can we create?

Question

A cubic graph is a graph, whose vertices are all of degree 3. A bicubic graph is a cubic graph that is bipartite.

The picture below shows the smallest bicubic graph. The only one with 6 vertices.

It's easy to notice that every bicubic graph has an even number of vertices. My question is: how many bicubic graphs of n vertices are there?

Answer 1

Just like @Robert said in the comment, the problem is hard. The only known solution is up to n = 28:

n  bicubic(n)
6  1
8  1
10 2
12 6
14 14
16 41
18 157
20 725
22 4196
24 29816
26 246644
28 2297075
30 23503477
32 260265023