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A128769
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Number of inequivalent n-colorings of the 6D hypercube under the full orthogonal group of the cube (of order 2^6*6! = 46080).
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0
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1, 400507806843728, 74515759884862073604656433, 7384600028168436080716029918923776, 11764346491956060465118857334844472390625, 1374572193221502774409273556832082839526247376
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OFFSET
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1,2
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COMMENTS
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I assume this refers to colorings of the vertices of the cube. - N. J. A. Sloane, Apr 06 2007
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REFERENCES
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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.
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.
Polya, G. & Read R. C. Combinatorial Enumeration of Groups, Graphs and Chemical Compounds. Springer-Verlag, 1987.
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LINKS
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FORMULA
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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)
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EXAMPLE
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a(2)=400507806843728 because there are 400507806843728 inequivalent 2-colorings of the 6D hypercube.
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MATHEMATICA
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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)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Ricardo Perez-Aguila (ricardo.perez.aguila(AT)gmail.com), Apr 04 2007
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STATUS
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approved
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