The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 n-dimensional 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Rows 1 through 4 computed by Veit Elser, later confirmed by Tom Karzes. The row sums give A333539. REFERENCES N. J. A. Sloane, Cutting Up a Cube, Math Fun Mailing List, Apr 10 2020; with replies from Tom Karzes, Tomas Rokicki, Veit Elser, and others. LINKS Table of n, a(n) for n=1..20. Veit Elser, Rows 1 through 4 Scott R. Shannon, Illustration for a(2) = 4. Scott R. Shannon, Illustration for a(3) = 72. This shows the 4-faced 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 5-faced 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 Cf. A333539, A333540, A333544, A338622 (number of k-faced polyhedra for the 3D Platonic solids). For the number of hyperplanes see A007847. Sequence in context: A354859 A088693 A322397 * A262235 A133003 A358293 Adjacent sequences: A333540 A333541 A333542 * A333544 A333545 A333546 KEYWORD nonn,tabf,more AUTHOR N. J. A. Sloane, Apr 21 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 05:10 EST 2023. Contains 367629 sequences. (Running on oeis4.)