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 A060530 Number of inequivalent ways to color edges of a cube using at most n colors. 7
 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; text; internal format)
 OFFSET 0,3 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. - JosÃ© H. Nieto S., Jan 19 2012 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). LINKS Harry J. Smith, Table of n, a(n) for n=0..200 Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1). 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.) G.f.: -x*(150*x^10 +19758*x^9 +425032*x^8 +2763481*x^7 +6769435*x^6 +6773089*x^5 +2763307*x^4 +423883*x^3 +20059*x^2 +205*x +1)/(x -1)^13. - Colin Barker, Aug 13 2012 MATHEMATICA Table[(n^12+6n^7+3n^6+8n^4+6n^3)/24, {n, 0, 20}] (* Harvey P. Dale, Feb 13 2013 *) 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); ) } \\ Harry J. Smith, Jul 06 2009 CROSSREFS Cf. A000543 (vertices), A047780 (faces). See A199406 for number of orbits under a different symmetry group. - N. J. A. Sloane, Aug 14 2012 Sequence in context: A224741 A209824 A230333 * A252997 A126829 A171406 Adjacent sequences:  A060527 A060528 A060529 * A060531 A060532 A060533 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 11 2001 EXTENSIONS Entry revised by N. J. A. Sloane, Jan 03 2005 STATUS approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)