A080658 Order of group of n X n X n Rubik cube, under assumptions not-s, not-m, i.

1, 3674160, 43252003274489856000, 326318176648849198250599213408124182588293120000000000, 6117367460827460912265057790940131872699535863380422035173008779767508369408000000000000000000

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 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.

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. 33-43, 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

Maple

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 := 0; 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;

Crossrefs

See A007458, A054434, A075152, A074914, A080656-A080662 for other versions.

Sequence in context: A271027 A080657 A075152 * A080656 A074914 A080661

Adjacent sequences: A080655 A080656 A080657 * A080659 A080660 A080661

Keyword

nonn

Author

N. J. A. Sloane, Mar 01 2003

Status

approved