%N Order of group of n X n X n Rubik cube, under assumptions s, not-m, i.
%C The three possible assumptions considered here are the following:
%C s (for n odd) indicates that we are working in the "supergroup" and so take account of twists of the face centers.
%C 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.
%C 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.
%D Dan Hoey, posting to Cube Lovers List, Jun 24, 1987.
%D 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.
%H Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-6.gz">Cube Lovers Archive, Part 6</a>
%p f := proc(n) local A,B,C,D,E,F,G; if n mod 2 = 1 then A := (n-1)/2; F := 0; B := (n-1)/2; C := (n-1)/2; D := (n-1)/2; E := (n+4)*(n-1)*(n-3)/24; G := (n^2-1)*(n-3)/24; else A := n/2; F := 1; B := n/2; C := 0; D := 0; E := n*(n^2-4)/24; G := n*(n-1)*(n-2)/24; 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;
%Y See A007458, A054434, A075152, A074914, A080656-A080661 for other versions.
%A _N. J. A. Sloane_, Mar 01 2003