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 A080660 Order of group of n X n X n Rubik cube, under assumptions s, m, not-i. 0
 1, 3674160, 88580102706155225088000, 707195371192426622240452051915172831683411968000000000, 5289239086872492808525454741861751983960246149231077646632506991757159229816832000000000000000 (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 Alan Bawden, Cube Lovers Archive, Part 6 FORMULA a(1)=1 ;a(2)=7!*3^6; a(3)=8!*3^7*12!*2^10*4^6/2; a(n)=a(n-2)*24!*(24!/2)^(n-3). - Herbert Kociemba, Dec 08 2016 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 := 1; C := 1; D := 1; E := (n+1)*(n-3)/4; G := 0; else A := n/2; F := 1; B := 1; C := 0; D := 0; E := n*(n-2)/4; 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; MATHEMATICA f=1; f=7!3^6; f=8!3^7 12!2^10 4^6/2; f[n_]:=f[n-2]*24!(24!/2)^(n-3); Table[f[n], {n, 1, 10}] (* Herbert Kociemba, Dec 08 2016 *) CROSSREFS See A007458, A054434, A075152, A074914, A080656-A080662 for other versions. Sequence in context: A074914 A080661 A080662 * A080659 A328215 A216002 Adjacent sequences:  A080657 A080658 A080659 * A080661 A080662 A080663 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 01 2003 STATUS approved

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Last modified February 24 00:51 EST 2020. Contains 332195 sequences. (Running on oeis4.)