A368031 Number of free treelike midpoint-free polycubes of size n, identifying rotations and reflections.

1, 1, 1, 3, 4, 12, 23, 47, 91, 202, 428, 911, 1862, 3638, 6637, 11780, 20764, 36904, 64855, 111552, 186147, 302526, 479076, 739080, 1106514, 1610045, 2278632, 3146000, 4254002, 5682571, 7558064, 10081716, 13532752, 18293656, 24830210, 33733178, 45720871

Offset: 1

Author

Joerg Arndt, Dec 08 2023

Keywords

• nonn

Comments

Treelike means that the graph connecting midpoints of adjacent cubes has no cycles.

Midpoint-free means that no three cubes are in positions (x,y,z), (x+dx,y+dx,z+dz), and (x+2*dx,y+2*dx,z+2*dz).

Examples

			The polycubes for n <= 5 are:
n=1:
  0,0,0
n=2:
  0,0,0; 0,0,1
n=3:
  0,0,0; 0,0,1; 0,1,0
n=4:
  0,0,0; 0,0,1; 0,1,0; 1,0,0
  0,0,0; 0,0,1; 0,1,0; 1,0,1
  0,0,0; 0,0,1; 0,1,1; 0,1,2
n=5:
  0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,0,2
  0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,1,0
  0,0,0; 0,0,1; 0,1,1; 0,1,2; 1,0,1
  0,0,0; 0,0,1; 0,1,1; 1,1,1; 1,1,2
		

Crossrefs

Cf. A304196, A368029.