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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. - José 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.)