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%I #10 Apr 15 2013 02:41:33
%S 1,400507806843728,74515759884862073604656433,
%T 7384600028168436080716029918923776,
%U 11764346491956060465118857334844472390625,1374572193221502774409273556832082839526247376
%N Number of inequivalent n-colorings of the 6D hypercube under the full orthogonal group of the cube (of order 2^6*6! = 46080).
%C I assume this refers to colorings of the vertices of the cube. - _N. J. A. Sloane_, Apr 06 2007
%D Banks, D. C.; Linton, S. A. & Stockmeyer, P. K. Counting Cases in Substitope Algorithms. IEEE Transactions on Visualization and Computer Graphics, Vol. 10, No. 4, pp. 371-384, 2004.
%D Perez-Aguila, Ricardo. Enumerating the Configurations in the n-Dimensional Orthogonal Polytopes Through Polya's Countings and A Concise Representation. Proceedings of the 3rd International Conference on Electrical and Electronics Engineering and XII Conference on Electrical Engineering ICEEE and CIE 2006, pp. 63-66.
%D Polya, G. & Read R. C. Combinatorial Enumeration of Groups, Graphs and Chemical Compounds. Springer-Verlag, 1987.
%H Banks, D. C.; Linton, S. A. & Stockmeyer, P. K., <a href="http://www.cs.fsu.edu/~banks/">Counting Cases in Substitope Algorithms</a>, IEEE Transactions on Visualization and Computer Graphics, Vol. 10, No. 4, pp. 371-384. 2004.
%H Perez-Aguila, Ricardo, <a href="http://ricardo.perez.aguila.googlepages.com/ricardoperez-aguila,phdthesis-orthogonalpolytopes:studyandapplication2">Orthogonal Polytopes: Study and Application</a>, PhD Thesis. Universidad de las Americas, Puebla. November, 2006.
%H Perez-Aguila, Ricardo, <a href="http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isnumber=4017927&arnumber=4017934&count=140&index=6">Enumerating the Configurations in the n-Dimensional Orthogonal Polytopes Through Polya's Countings and A Concise Representation</a>, Proceedings of the 3rd International Conference on Electrical and Electronics Engineering and XII Conference on Electrical Engineering ICEEE and CIE 2006, pp. 63-66.
%F a(n) = (1/46080)*(3840*n^6 + 16512*n^8 + 1920*n^12 + 3840*n^14 + 12504*n^16 + 2160*n^20 + 1440*n^22 + 2320*n^24 + 1213*n^32 + 120*n^36 + 180*n^40 + 30*n^48 + n^64)
%e a(2)=400507806843728 because there are 400507806843728 inequivalent 2-colorings of the 6D hypercube.
%t A[n_] := (1/46080)*(3840n^6 + 16512*n^8 + 1920*n^12 + 3840*n^14 + 12504*n^16 + 2160*n^20 + 1440*n^22 + 2320*n^24 + 1213*n^32 + 120*n^36 + 180*n^40 + 30*n^48 + n^64)
%o (PARI) a(n) = (1/46080)*(3840*n^6 + 16512*n^8 + 1920*n^12 + 3840*n^14 + 12504*n^16 + 2160*n^20 + 1440*n^22 + 2320*n^24 + 1213*n^32 + 120*n^36 + 180*n^40 + 30*n^48 + n^64); \\ _Joerg Arndt_, Apr 15 2013
%Y Cf. A000616, A002817.
%K nonn,easy
%O 1,2
%A Ricardo Perez-Aguila (ricardo.perez.aguila(AT)gmail.com), Apr 04 2007
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