

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)



OFFSET

0,3


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.
A halfturn is considered to be 2 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.


LINKS

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 QuarterTurn Metric
Tomas Rokicki, Symmetrical Positions


CROSSREFS

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


KEYWORD

nonn,fini


AUTHOR

N. J. A. Sloane, Feb 25 2003


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


STATUS

approved



