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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. 3
1, 1, 5, 25, 219, 1978, 18395, 171529, 1601725, 14956266, 139629194, 1303138445, 12157779067, 113382522382, 1056867697737, 9843661720634, 91532722388023, 846837132071729, 7668156860181597 (list; graph; refs; listen; history; text; internal format)



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.

A half-turn is considered to be 2 moves.

The total number of inequivalent positions is 901083404981813616. - Jerry Bryan, Mar 03 2003.


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


Table of n, a(n) for n=0..18.

Alan Bawden, Cube Lovers Archive, Part 15

Alan Bawden, Cube Lovers Archive, Part 16

Alan Bawden, Cube Lovers Archive, Part 26

Tomas Rokicki, God's Number in the Quarter-Turn Metric

Tomas Rokicki, Symmetrical Positions


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

Sequence in context: A080632 A245166 A144575 * A061839 A143600 A209529

Adjacent sequences:  A005449 A005450 A005451 * A005453 A005454 A005455




N. J. A. Sloane, Feb 25 2003


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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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)