A368029 -id:A368029 - cp's OEIS frontend

A368030 Number of fixed midpoint-free polycubes of size n.

1, 3, 12, 47, 168, 532, 1344, 2707, 5064, 11236, 24768, 53614, 112464, 222564, 411008, 723884, 1263696, 2236452, 3953448, 6855498, 11544816, 18880992, 30104592, 46815126, 70776080, 103864092, 148069152, 205499496, 278917752, 373204912, 496855592, 663056406, 890682648, 1205069272

Offset: 1

Joerg Arndt, Dec 08 2023

nonn

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).

Cf. A368029.

A368031 Number of free treelike midpoint-free polycubes of size n, identifying rotations and reflections.

Original entry on oeis.org

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

Joerg Arndt, Dec 08 2023

nonn

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).

			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

Cf. A304196, A368029.

cp's OEIS Frontend

A368030 Number of fixed midpoint-free polycubes of size n.

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