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.

Showing 1-3 of 3 results.

A080601 Number of positions of the Rubik's cube at a distance of n moves from the solved state, in the half-turn metric.

Original entry on oeis.org

1, 18, 243, 3240, 43239, 574908, 7618438, 100803036, 1332343288, 17596479795, 232248063316, 3063288809012, 40374425656248, 531653418284628, 6989320578825358, 91365146187124313
Offset: 0

Views

Author

N. J. A. Sloane, Feb 25 2003

Keywords

Comments

The half-turn metric counts both quarter-turns and half-turns as 1 move.
This is the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves.
The total number of positions is (8!*12!/2)*(2^12/2)*(3^8/3) = 43252003274489856000. - Jerry Bryan, Mar 03 2003
Relationship with A080583: 243 = 262 - 18 - 1, 3240 = 3502 - 262, 43239 = 46741 - 3502, ...

References

  • Robert G. Bryan (Jerry Bryan), posting to Cube Lovers List, Jul 10, 1998.
  • Rokicki, Tomas. Thirty years of computer cubing: The search for God's number. 2014. Reprinted in "Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rogers", ed. Thane Plambeck and Tomas Rokicki, MAA Press, 2020, pp. 79-98. See Table 9.4.
  • Rokicki, T., Kociemba, H., Davidson, M., & Dethridge, J. (2014). The diameter of the rubik's cube group is twenty. SIAM REVIEW, 56(4), 645-670. See Table 5.1.

Crossrefs

Extensions

a(11) (from Jerry Bryan, 2006) and a(12) (from Tom Rokicki, 2009) added by Herbert Kociemba, Jun 24 2009
a(13) added by Tomas Rokicki, Jul 25 2009
a(14) (from Thomas Scheunemann) and a(15) (from Morley Davidson, John Dethridge, Herbert Kociemba, and Tomas Rokicki) added by Tomas Rokicki, Jul 29 2010
Name edited by Charles R Greathouse IV, Jan 19 2016
Name edited by Ben Whitmore, Jul 31 2024

A080602 Number of positions of the Rubik's cube at a distance of n moves from the solved state, in the quarter-turn metric.

Original entry on oeis.org

1, 12, 114, 1068, 10011, 93840, 878880, 8221632, 76843595, 717789576, 6701836858, 62549615248, 583570100997, 5442351625028, 50729620202582, 472495678811004, 4393570406220123, 40648181519827392, 368071526203620348
Offset: 0

Views

Author

N. J. A. Sloane, Feb 25 2003

Keywords

Comments

The quarter-turn metric counts quarter-turns as 1 move and half-turns as 2 moves.
This is the number of positions that can be reached in n quarter-turns from the start, but which cannot be reached in fewer than n quarter-turns.
The total number of positions is (8!*12!/2)*(2^12/2)*(3^8/3) = 43252003274489856000. - Jerry Bryan, Mar 03 2003

References

  • Robert G. Bryan (Jerry Bryan), postings to Cube Lovers List, Feb 04, 1995 and Oct 26, 1998.
  • Rokicki, Tomas. Thirty years of computer cubing: The search for God's number. 2014. Reprinted in "Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rogers", ed. Thane Plambeck and Tomas Rokicki, MAA Press, 2020, pp. 79-98. See Table 9.5.

Crossrefs

Extensions

Added a(14) and a(15) from my earlier investigations, confirmed by Scheunemann, and also added his result for a(16). - Tomas Rokicki, Jul 14 2010
Added a(17) from Thomas Scheunemann, a(18) from my God's Number investigations, corrected some links. - Tomas Rokicki, Sep 01 2014
Name edited by Charles R Greathouse IV, Jan 19 2016
Name edited by Ben Whitmore, Aug 02 2024

A005452 Number of positions that the 3 X 3 X 3 Rubik cube puzzle can be in after exactly n moves, up to equivalence under the full group of order 48 of the cube and with a half-turn is considered to be 2 moves.

Original entry on oeis.org

1, 1, 5, 25, 219, 1978, 18395, 171529, 1601725, 14956266, 139629194, 1303138445, 12157779067, 113382522382, 1056867697737, 9843661720634, 91532722388023, 846837132071729, 7668156860181597
Offset: 0

Views

Author

N. J. A. Sloane, Feb 25 2003

Keywords

Comments

This is the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves.
The total number of inequivalent positions is 901083404981813616. - Jerry Bryan, Mar 03 2003

References

  • Robert G. Bryan (Jerry Bryan), postings to Cube Lovers List, Feb 04, 1995 and Oct 26, 1998.

Crossrefs

This is A080602 reduced by action of group of order 48. Cf. A080583, A080601, A080638.

Extensions

Added a(13)-a(18). This is based on a great deal of work by a large number of people; full links and credit are on cube20.org/qtm. The numbers were calculated by combining the God's number counts on the main page with the symmetric solution counts on the symmetry page. - Tomas Rokicki, Sep 01 2014
Showing 1-3 of 3 results.