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
- 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.
- Alan Bawden, Cube Lovers Archive, Part 25
- Jerry Bryan, God's Algorithm...
- David Dijon, The insanely large number of Rubik's cube permutations | MegaFavNumbers, video (2020)
- Mark Longridge, God's Algorithm Calculations for Rubik's Cube...
- Tomas Rokicki, God's Algorithm out to 13f*
- Tomas Rokicki, God's Number is 20
- T. Rokicki, Twenty-two moves suffice for Rubik's Cube, Math. Intell. 32 (1) (2010) 33-40.
- T. Rokicki, 15f* in the Face Turn Metric.
- T. Rokicki, God's Algorithm out to 14f*
- Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge, The Diameter Of The Rubik's Cube Group Is Twenty, SIAM J. of Discrete Math, Vol. 27, No. 2 (2013), pp. 1082-1105.
a(11) (from Jerry Bryan, 2006) and a(12) (from Tom Rokicki, 2009) added by
Herbert Kociemba, Jun 24 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
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
- 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.
- Alan Bawden, Cube Lovers Archive, Part 15
- Alan Bawden, Cube Lovers Archive, Part 26
- Mark Longridge, God's Algorithm Calculations for Rubik's Cube...
- Tomas Rokicki, God's Algorithm out to 15q*. Posted Sep 26 2009. - _Tomas Rokicki_, Jul 14 2010
- Thomas Scheunemann, God's Algorithm out to 16q*. Posted Jul 09 2010. - _Tomas Rokicki_, Jul 14 2010
- Thomas Scheunemann, God's Algorithm out to 17q*. Posted Jul 09 2010. - _Tomas Rokicki_, Jul 14 2010
- Tomas Rokicki, God's Algorithm out to 18q*. Posted Jul 19 2014.
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
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
- Robert G. Bryan (Jerry Bryan), postings to Cube Lovers List, Feb 04, 1995 and Oct 26, 1998.
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
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