login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080659 Order of group of n X n X n Rubik cube, under assumptions s, m, i. 0
1, 3674160, 88580102706155225088000, 31180187340244394380451751732775816935095098996162560000000000, 234260670776288045954071997895225719627421688127737132331392149764072811894713478221812860985540608000000000000000000 (list; graph; refs; listen; history; text; internal format)
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 := (n-1)/2; E := (n+4)*(n-1)*(n-3)/24; G := 0; else A := n/2; F := 1; B := n/2; C := 0; D := 0; E := n*(n^2-4)/24; 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;

CROSSREFS

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

Sequence in context: A080661 A080662 A080660 * A216002 A187644 A136287

Adjacent sequences:  A080656 A080657 A080658 * A080660 A080661 A080662

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 01 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 21:33 EST 2016. Contains 278755 sequences.