%I A128769
%S A128769 1,400507806843728,74515759884862073604656433,
%T A128769 7384600028168436080716029918923776,
%U A128769 11764346491956060465118857334844472390625
%N A128769 Number of inequivalent n-colorings of the 6D hypercube under the full 
               orthogonal group of the cube (of order 2^6*6! = 46080).
%C A128769 I assume this refers to colorings of the vertices of the cube. - N. J. 
               A. Sloane (njas(AT)research.att.com), Apr 06 2007
%D A128769 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 A128769 Perez-Aguila, Ricardo. Enumerating the Configurations in the n-Dimensional 
               Orthogonal Polytopes Through Polya's Counting 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 A128769 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 A128769 Polya, G. & Read R. C. Combinatorial Enumeration of Groups, Graphs and 
               Chemical Compounds. Springer-Verlag, 1987.
%H A128769 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 A128769 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 A128769 Perez-Aguila, Ricardo, <a href="http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isnumber=4017927&arnumber=4017\
               934&count=140&index=6">Enumerating the Configurations in the n-Dimensional 
               Orthogonal Polytopes Through Polya's Counting 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 A128769 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)
%e A128769 a(2)=400507806843728 because there are 400507806843728 inequivalent 2-colorings 
               of the 6D hypercube.
%t A128769 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)
%Y A128769 Cf. A000616, A002817.
%Y A128769 Sequence in context: A080125 A082589 A011528 this_sequence A086438 A104873 
               A088867
%Y A128769 Adjacent sequences: A128766 A128767 A128768 this_sequence A128770 A128771 
               A128772
%K A128769 nonn
%O A128769 1,2
%A A128769 Ricardo Perez-Aguila (ricardo.perez.aguila(AT)gmail.com), Apr 04 2007