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A368029
Number of free midpoint-free polycubes of size n, identifying rotations and reflections.
2
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).
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
KEYWORD
nonn,more
AUTHOR
Joerg Arndt , Dec 08 2023
STATUS
approved