A363204 -id:A363204 - cp's OEIS frontend

A363203 Number of free linear polycubes of size n, identifying rotations and reflections and avoiding neighbors at [0,0,+-2], [0,+-2,0], and [+-2,0,0].

1, 1, 1, 2, 4, 9, 20, 51, 128, 338, 882, 2350, 6238, 16693, 44561, 119339, 319104, 854420, 2285357

Offset: 1

Joerg Arndt and Márk Péter Légrádi, May 21 2023

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

When a cube [x,y,z] is in the polycube then neither of the six cubes [x+-2,y,z], [x,y+-2,z], [x,y,z+-2] can be in the polycube. For example, no three cubes can be in a row.

Cf. A363204 (linear and avoiding at [+-1,+-1,+-1]).

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

Original entry on oeis.org

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

Joerg Arndt , Dec 08 2023

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 <= 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

Cf. A368030, A363203, A363204, A363207.

cp's OEIS Frontend

A363203 Number of free linear polycubes of size n, identifying rotations and reflections and avoiding neighbors at [0,0,+-2], [0,+-2,0], and [+-2,0,0].

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