cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

A080659 Order of group of n X n X n Rubik cube, under assumptions s, m, i.

Original entry on oeis.org

1, 3674160, 88580102706155225088000, 31180187340244394380451751732775816935095098996162560000000000, 234260670776288045954071997895225719627421688127737132331392149764072811894713478221812860985540608000000000000000000
Offset: 1

Views

Author

N. J. A. Sloane, Mar 01 2003

Keywords

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

Crossrefs

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

Programs

  • 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;

A080660 Order of group of n X n X n Rubik cube, under assumptions s, m, not-i.

Original entry on oeis.org

1, 3674160, 88580102706155225088000, 707195371192426622240452051915172831683411968000000000, 5289239086872492808525454741861751983960246149231077646632506991757159229816832000000000000000
Offset: 1

Views

Author

N. J. A. Sloane, Mar 01 2003

Keywords

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

Crossrefs

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

Programs

  • 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]=1;f[2]=7!3^6;f[3]=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 *)

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

A256573 God's number for Rubik's cube size n X n X n (quarter-turn metric).

Original entry on oeis.org

0, 14, 26
Offset: 1

Views

Author

Peter Woodward, Apr 22 2015

Keywords

Comments

"God's Number" is the maximum number of turns required to solve any scramble of cube. "Quarter-turn metric" considers a 90-degree turn of any side to be a single turn, while a 180-degree turn is considered two turns. Cubes of larger size than 3 X 3 X 3 are not solved for God's number.

Links

Crossrefs

Cf. A257401 (half-turn metric), A054434 (possible positions), A075152 (possible permutations).

A330389 Maximal order of an element in the n X n X n Rubik's cube group.

Original entry on oeis.org

45, 1260, 765765, 281801520, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880
Offset: 2

Views

Author

Dmitry Kamenetsky, Dec 13 2019

Keywords

Comments

For the standard Rubik's cube (n = 3) the longest period 1260 is obtained with the moves RU2D'BD'.
a(n) = a(6) for all n > 6.

Links

Crossrefs

Cf. A007458, A054434, A075152, A257401.
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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