cp's OEIS Frontend

A080656 Order of group of n X n X n Rubik cube, under assumptions not-s, m, not-i.

%I A080656 #18 Jul 04 2022 08:00:38
%S A080656 1,3674160,43252003274489856000,
%T A080656 707195371192426622240452051915172831683411968000000000,
%U A080656 2582636272886959379162819698174683585918088940054237132144778804568925405184000000000000000
%N A080656 Order of group of n X n X n Rubik cube, under assumptions not-s, m, not-i.
%C A080656 The three possible assumptions considered here are the following:
%C A080656 s (for n odd) indicates that we are working in the "supergroup" and so take account of twists of the face centers.
%C A080656 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 A080656 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 A080656 Dan Hoey, posting to Cube Lovers List, Jun 24, 1987.
%D A080656 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 A080656 Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-6.gz">Cube Lovers Archive, Part 6</a>
%F A080656 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
%p A080656 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;
%t A080656 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); Array[f,5] (* _Herbert Kociemba_, Dec 08 2016 *)
%t A080656 f[1]=1;f[n_]:=7!3^6(6*24!!)^(s=Mod[n,2])24!^(r=(n-s)/2-1)(24!/2)^(r(r+s)); Array[f,5] (* _Herbert Kociemba_, Jul 03 2022 *)
%Y A080656 See A007458, A054434, A075152, A074914, A080658, A080659, A080660, A080661, A080662 for other versions.
%K A080656 nonn
%O A080656 1,2
%A A080656 _N. J. A. Sloane_, Mar 01 2003