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%I #14 Dec 10 2023 15:18:01
%S 1,1,1,3,4,12,23,47,91,202,428,911,1862,3638,6637,11780,20764,36904,
%T 64855,111552,186147,302526,479076,739080,1106514,1610045,2278632,
%U 3146000,4254002,5682571,7558064,10081716,13532752,18293656,24830210,33733178,45720871
%N Number of free treelike midpoint-free polycubes of size n, identifying rotations and reflections.
%C Treelike means that the graph connecting midpoints of adjacent cubes has no cycles.
%C 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).
%e The polycubes for n <= 5 are:
%e n=1:
%e 0,0,0
%e n=2:
%e 0,0,0; 0,0,1
%e n=3:
%e 0,0,0; 0,0,1; 0,1,0
%e n=4:
%e 0,0,0; 0,0,1; 0,1,0; 1,0,0
%e 0,0,0; 0,0,1; 0,1,0; 1,0,1
%e 0,0,0; 0,0,1; 0,1,1; 0,1,2
%e n=5:
%e 0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,0,2
%e 0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,1,0
%e 0,0,0; 0,0,1; 0,1,1; 0,1,2; 1,0,1
%e 0,0,0; 0,0,1; 0,1,1; 1,1,1; 1,1,2
%Y Cf. A304196, A368029.
%K nonn
%O 1,4
%A _Joerg Arndt_, Dec 08 2023
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