|
| |
|
|
A129668
|
|
Number of different ways to divide an n X n X n cube into subcubes.
|
|
1
| | |
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| The Hadwiger problem analyzes how to divide a cube into n subcubes. This sequence analyzes in how many different ways the n X n X n cube can be divided into subcubes
One of the 1656 possible divisions of the 8 x 8 x 8 cube (42 of 1x1x1; 4 of 2x2x2; 2 of 3x3x3 and 6 of 4x4x4) solves the last unknown of the Hadwiger problem, n=54, found in 1973
|
|
|
LINKS
| Mathworld, Hadwiger Problem.
Mathworld, Cube Dissection.
|
|
|
EXAMPLE
| a(3)=3 because the 3 X 3 X 3 cube can be divided into subcubes in 3 different ways: a single 3 X 3 X 3 cube, a 2 X 2 X 2 plus 19 1 X 1 X 1 cubes or into 27 1 X 1 X 1 cubes. a(4)=11 because the 4 X 4 X 4 cube can be divided into 11 different combinations of subcubes such as 64 1 X 1 X 1 cubes, or 8 2 X 2 X 2 cubes, etc.
|
|
|
CROSSREFS
| Cf. A014544.
Sequence in context: A051083 A051097 A076201 * A086791 A004687 A097895
Adjacent sequences: A129665 A129666 A129667 * A129669 A129670 A129671
|
|
|
KEYWORD
| hard,more,nonn,nice
|
|
|
AUTHOR
| Sergio Pimentel (ferdiego(AT)suddenlink.net), May 02 2008, Jun 03 2008
|
| |
|
|
