A368032 Number of free linear midpoint-free polycubes of size n, identifying rotations and reflections.

1, 1, 1, 2, 3, 7, 11, 20, 34, 65, 113, 197, 315, 488, 685, 1002, 1409, 2019, 2679, 3667, 4837, 6558, 8474, 11018, 13786, 17882, 22431, 28918, 36411, 46905, 59183, 76343, 96372, 123464, 153738, 193710, 237629, 294513, 357010, 436593

Offset

1,4

Comments

Linear polycubes have two end points with one neighbor, the remaining cubes all have two neighbors.

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..40.

Example

The polycubes for n <= 6 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; 1,0,1
  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; 1,1,1; 1,1,2
n=6:
  0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,0,2; 1,1,0
  0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,0,2; 1,1,2
  0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,1,1; 1,1,2
  0,0,0; 0,0,1; 0,1,1; 0,1,2; 1,1,2; 1,1,3
  0,0,0; 0,0,1; 0,1,1; 0,1,2; 1,1,2; 1,2,2
  0,0,0; 0,0,1; 0,1,1; 1,1,1; 1,1,2; 1,2,2
  0,0,0; 0,0,1; 0,1,1; 1,1,1; 1,2,1; 1,2,2

Crossrefs

Cf. A368031.

Sequence in context: A160434 A139630 A245738 * A265093 A133044 A014529

Adjacent sequences: A368029 A368030 A368031 * A368033 A368034 A368035

Keyword

nonn

Author

Joerg Arndt, Dec 09 2023

Status

approved