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Search: id:A129668
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| A129668 |
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Number of different ways to divide an n X n X n cube into subcubes. |
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+0
2
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OFFSET
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1,2
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COMMENT
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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
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LINKS
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Mathworld, Hadwiger Problem.
Mathworld, Cube Dissection.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A014544.
Sequence in context: A051083 A051097 A076201 this_sequence A086791 A004687 A097895
Adjacent sequences: A129665 A129666 A129667 this_sequence A129669 A129670 A129671
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KEYWORD
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hard,more,nonn,nice
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AUTHOR
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Sergio Pimentel (ferdiego(AT)suddenlink.net), May 02 2008, Jun 03 2008
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