A368031 -id:A368031 - cp's OEIS frontend

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

Joerg Arndt, Dec 09 2023

nonn

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).

			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

Cf. A368031.

cp's OEIS Frontend

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

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