User blog:SuperSpruce/Idea for a non-recursive function

Here we go: a non-recursive function. But I think this doesn’t even reach f_3(x)

B(x)= the number of different designs one could make with x x-dimensional blocks (line with length 1, square with side length 1, cube with edge length 1, etc.) fully connected to each other. With lines, they could connect at the endpoints. With squara, they could connect their sides, but not just at 1 corner. With cubes, they could connect at their faces, but not just edges or corners. You get the idea. Blocks cannot overlap each other.

B(1)= 1

B(2)= 1

B(3)= 2

B(4)= maybe 7?