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A060530
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Number of inequivalent ways to color edges of a cube using at most n colors.
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4
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0, 1, 218, 22815, 703760, 10194250, 90775566, 576941778, 2863870080, 11769161895, 41669295250, 130772947481, 371513523888, 970769847320, 2362273657030, 5406141568500, 11728193258496, 24276032182173, 48201464902410, 92221684354915
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Here inequivalent means under the action of the rotation group of the cube, of order 24, which in its action on the edges has cycle index (x1^12 + 3*x2^6 + 6*x4^3 + 6*x1^2*x2^5 + 8*x3^4)/24.
Also, number of inequivalent colorings of the edges of a regular octahedron using at most n colors. - José H. Nieto S., Jan 19 2012
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REFERENCES
| N. G. De Bruijn, Polya's theory of counting, in E. F. Beckenbach, ed., Applied Combinatorial Mathematics, Wiley, 1964, pp. 144-184 (see p. 147).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
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FORMULA
| a(n) = (n^12+6*n^7+3*n^6+8*n^4+6*n^3)/24. (Replace all x_i's in the cycle index by n.)
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PROG
| (PARI) { for (n=0, 200, write("b060530.txt", n, " ", (n^12 + 6*n^7 + 3*n^6 + 8*n^4 + 6*n^3)/24); ) } [From Harry J. Smith, Jul 06 2009]
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CROSSREFS
| Cf. A000543 (vertices), A047780 (faces).
Sequence in context: A038595 A045239 A185462 * A126829 A171406 A025406
Adjacent sequences: A060527 A060528 A060529 * A060531 A060532 A060533
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 11 2001
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Jan 03 2005
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