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A075152
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Number of possible permutations of a Rubik cube of size n X n X n.
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12
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OFFSET
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1,2
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COMMENTS
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More precisely, order of group of n X n X n Rubik cube, under assumptions not-s, not-m, not-i.
The three possible assumptions considered here are the following:
s (for n odd) indicates that we are working in the "supergroup" and so take account of twists of the face centers.
m (for n > 3) indicates that the pieces are marked so that we take account of the permutation of the identically-colored pieces on a face.
i (for n > 3) indicates that we are working in the theoretical invisible group and solve the pieces on the interior of the cube as well as the exterior. It is assumed that the M and S traits apply to the interior pieces as if they were on the exterior of a smaller cube.
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REFERENCES
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Dan Hoey, posting to Cube Lovers List, Jun 24, 1987.
Rowley, Chris, The group of the Hungarian magic cube, in Algebraic structures and applications (Nedlands, 1980), pp. 33-43, Lecture Notes in Pure and Appl. Math., 74, Dekker, New York, 1982.
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LINKS
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_Robert G. Wilson v_, Table of n, a(n) for n = 1..10 . [From Robert G. Wilson v, May 23 2009]
Answers.com, Rubik's Cube . [From Robert G. Wilson v, May 23 2009]
Alan Bawden, Cube Lovers Archive, Part 6
.docstoc, How to Solve a Rubiks Cube . [From Robert G. Wilson v, May 23 2009]
Christophe Goudey, Informtion . [From Robert G. Wilson v, May 23 2009]
Uwe Meffert, Meffert's Puzzles
Jaap Scherphuis, Puzzle Pages
Eric Weisstein's World of Mathematics, Rubik's Cube . [From Robert G. Wilson v, May 23 2009]
WikiHow, How to Solve a Rubik's Cube with the Layer Method . [From Robert G. Wilson v, May 23 2009]
Wikipedia, Professor's Cube . [From Robert G. Wilson v, May 23 2009]
Wikipedia, Professor's Cube . [From Robert G. Wilson v, May 23 2009]
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MAPLE
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f := proc(n) local A, B, C, D, E, F, G; if n mod 2 = 1 then A := (n-1)/2; F := 0; B := 1; C := 1; D := 0; E := (n+1)*(n-3)/4; G := (n-1)*(n-3)/4; else A := n/2; F := 1; B := 1; C := 0; D := 0; E := n*(n-2)/4; G := (n-2)^2/4; fi; (2^A*((8!/2)*3^7)^B*((12!/2)*2^11)^C*((4^6)/2)^D*(24!/2)^E)/(24^F*((24^6)/2)^G); end;
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MATHEMATICA
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f[n_] := Block[{a, b, c, d, e, f, g}, If[OddQ@ n, a = (n - 1)/2; b = c = 1; d = f = 0; e = (n + 1) (n - 3)/4; g = (n - 1) (n - 3)/4, a = n/2; b = f = 1; c = d = 0; e = n (n - 2)/4; g = (n - 2)^2/4]; Ceiling[(2^a*((8!/2)*3^7)^b*((12!/2)*2^11)^c*((4^6)/2)^d*(24!/2)^e)/(24^f*((24^6)/2)^g)]]; Array[f, 10] [From Robert G. Wilson v, May 23 2009]
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CROSSREFS
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See A007458, A054434, A075152, A074914, A080656-A080662 for other versions.
Sequence in context: A114686 A217673 A080657 * A080658 A080656 A074914
Adjacent sequences: A075149 A075150 A075151 * A075153 A075154 A075155
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KEYWORD
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nonn
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AUTHOR
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Warren Power (wjpnply(AT)hotmail.com), Sep 05 2002
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EXTENSIONS
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Entry revised by N. J. A. Sloane, Apr 01 2006
Offset changed to 1 by N. J. A. Sloane, Sep 02 2009
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STATUS
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approved
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