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A080660
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Order of group of n X n X n Rubik cube, under assumptions s, m, not-i.
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0
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1, 3674160, 88580102706155225088000, 707195371192426622240452051915172831683411968000000000, 5289239086872492808525454741861751983960246149231077646632506991757159229816832000000000000000
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OFFSET
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1,2
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COMMENTS
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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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Table of n, a(n) for n=1..5.
Alan Bawden, Cube Lovers Archive, Part 6
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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 := 1; E := (n+1)*(n-3)/4; G := 0; else A := n/2; F := 1; B := 1; C := 0; D := 0; E := n*(n-2)/4; G := 0; 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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CROSSREFS
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See A007458, A054434, A075152, A074914, A080656-A080662 for other versions.
Sequence in context: A074914 A080661 A080662 * A080659 A216002 A187644
Adjacent sequences: A080657 A080658 A080659 * A080661 A080662 A080663
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Mar 01 2003
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STATUS
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approved
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