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

1,4

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).

Links

Table of n, a(n) for n=1..37.

Example

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.

Sequence in context: A005221 A243391 A000206 * A240737 A075223 A071332

Adjacent sequences: A368028 A368029 A368030 * A368032 A368033 A368034

Keyword

nonn

Author

Joerg Arndt, Dec 08 2023

Status

approved