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A080656 Order of group of n X n X n Rubik cube, under assumptions not-s, m, not-i. 7
1, 3674160, 43252003274489856000, 707195371192426622240452051915172831683411968000000000, 2582636272886959379162819698174683585918088940054237132144778804568925405184000000000000000 (list; graph; refs; listen; history; text; internal format)



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.


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.


Table of n, a(n) for n=1..5.

Alan Bawden, Cube Lovers Archive, Part 6


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


f := proc(n) local A, B, C, D, E, F, G; if n mod 2 = 1 then A := (n-1)/2; B := 1; C := 1; D := 0; E := (n+1)*(n-3)/4; F := 0; G := 0; else A := n/2; B := 1; C := 0; D := 0; E := n*(n-2)/4; F := 1; 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;


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


See A007458, A054434, A075152, A074914, A080658-A080662 for other versions.

Sequence in context: A080657 A075152 A080658 * A074914 A080661 A080662

Adjacent sequences:  A080653 A080654 A080655 * A080657 A080658 A080659




N. J. A. Sloane, Mar 01 2003



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Last modified December 8 01:00 EST 2021. Contains 349590 sequences. (Running on oeis4.)