

A333543


Irregular triangle read by rows: T(n,k) (n >= 1, k >= n+1) is the number of cells with k vertices in the dissection of an ndimensional cube by all the hyperplanes that pass through any n vertices.


7



1, 4, 72, 24, 162816, 96576, 118464, 64896, 45888, 22464, 19776, 11904, 8640, 8448, 6144, 1728, 1152, 384, 384, 384
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OFFSET

1,2


COMMENTS



REFERENCES



LINKS

Scott R. Shannon, Illustration for a(3) = 72. This shows the 4faced cells in the 3D cube dissection. The 72 pieces have been moved away from the origin a distance proportional to the average distance of their vertices from the origin.
Scott R. Shannon, Illustration for a(4) = 24. This shows the 5faced cells in the 3D cube dissection. The 24 pieces have been moved away from the origin a distance proportional to the average distance of their vertices from the origin. These polyhedra form a perfect octahedron inside the original cube with its points touching the cube's inner surface.


EXAMPLE

The two diagonals of a square cut it into four triangular pieces, so T(2,3) = 4.
Triangle begins:
1,
4,
72, 24,
162816, 96576, 118464, 64896, 45888, 22464, 19776, 11904, 8640, 8448, 6144, 1728, 1152, 384, 384, 384,
...


CROSSREFS

For the number of hyperplanes see A007847.


KEYWORD

nonn,tabf,more


AUTHOR



STATUS

approved



