A128769 Number of inequivalent n-colorings of the 6D hypercube under the full orthogonal group of the cube (of order 2^6*6! = 46080).

1, 400507806843728, 74515759884862073604656433, 7384600028168436080716029918923776, 11764346491956060465118857334844472390625, 1374572193221502774409273556832082839526247376

Offset

1,2

Comments

I assume this refers to colorings of the vertices of the cube. - N. J. A. Sloane, Apr 06 2007

References

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.

Links

Table of n, a(n) for n=1..6.

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, Orthogonal Polytopes: Study and Application, PhD Thesis. Universidad de las Americas, Puebla. November, 2006.

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.

Formula

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)

Example

a(2)=400507806843728 because there are 400507806843728 inequivalent 2-colorings of the 6D hypercube.

Mathematica

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)

Prog

(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

Crossrefs

Cf. A000616, A002817.

Sequence in context: A172542 A198803 A317290 * A261150 A181392 A299799

Adjacent sequences: A128766 A128767 A128768 * A128770 A128771 A128772

Keyword

nonn,easy

Author

Ricardo Perez-Aguila (ricardo.perez.aguila(AT)gmail.com), Apr 04 2007

Status

approved