

A080660


Order of group of n X n X n Rubik cube, under assumptions s, m, noti.


0



1, 3674160, 88580102706155225088000, 707195371192426622240452051915172831683411968000000000, 5289239086872492808525454741861751983960246149231077646632506991757159229816832000000000000000
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OFFSET

1,2


COMMENTS

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 identicallycolored 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.


REFERENCES

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. 3343, Lecture Notes in Pure and Appl. Math., 74, Dekker, New York, 1982.


LINKS

Table of n, a(n) for n=1..5.
Alan Bawden, Cube Lovers Archive, Part 6


FORMULA

a(1)=1 ;a(2)=7!*3^6; a(3)=8!*3^7*12!*2^10*4^6/2; a(n)=a(n2)*24!*(24!/2)^(n3).  Herbert Kociemba, Dec 08 2016


MAPLE

f := proc(n) local A, B, C, D, E, F, G; if n mod 2 = 1 then A := (n1)/2; F := 0; B := 1; C := 1; D := 1; E := (n+1)*(n3)/4; G := 0; else A := n/2; F := 1; B := 1; C := 0; D := 0; E := n*(n2)/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;


MATHEMATICA

f[1]=1; f[2]=7!3^6; f[3]=8!3^7 12!2^10 4^6/2; f[n_]:=f[n2]*24!(24!/2)^(n3); Table[f[n], {n, 1, 10}] (* Herbert Kociemba, Dec 08 2016 *)


CROSSREFS

See A007458, A054434, A075152, A074914, A080656A080662 for other versions.
Sequence in context: A074914 A080661 A080662 * A080659 A328215 A216002
Adjacent sequences: A080657 A080658 A080659 * A080661 A080662 A080663


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mar 01 2003


STATUS

approved



