A368029 Number of free midpoint-free polycubes of size n, identifying rotations and reflections.

1, 1, 1, 4, 5, 18, 33, 70, 110, 246, 526, 1144, 2366, 4689, 8597, 15168, 26367, 46696, 82428, 142991, 240609, 393640, 627305, 975760, 1474671, 2164515, 3084956, 4282222, 5810980, 7776373, 10351373, 13815334, 18556147, 25107905

Offset

1,4

Comments

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..34.

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; 0,1,1
  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; 0,1,1; 1,0,0
  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. A368030, A363203, A363204, A363207.

Sequence in context: A357366 A026902 A026755 * A243120 A317378 A338866

Adjacent sequences: A368026 A368027 A368028 * A368030 A368031 A368032

Keyword

nonn,more

Author

Joerg Arndt , Dec 08 2023

Status

approved