%I A129668
%S A129668 1,2,3,11,19,121,291,1656
%N A129668 Number of different ways to divide an n X n X n cube into subcubes.
%C A129668 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
%C A129668 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
%H A129668 Mathworld, <a href="http://mathworld.wolfram.com/HadwigerProblem.html">
               Hadwiger Problem</a>.
%H A129668 Mathworld, <a href="http://mathworld.wolfram.com/CubeDissection.html">
               Cube Dissection</a>.
%e A129668 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.
%Y A129668 Cf. A014544.
%Y A129668 Sequence in context: A051083 A051097 A076201 this_sequence A086791 A004687 
               A097895
%Y A129668 Adjacent sequences: A129665 A129666 A129667 this_sequence A129669 A129670 
               A129671
%K A129668 hard,more,nonn,nice
%O A129668 1,2
%A A129668 Sergio Pimentel (ferdiego(AT)suddenlink.net), May 02 2008, Jun 03 2008