cp's OEIS Frontend

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.

%I A005452 #25 Jan 12 2025 17:37:52
%S A005452 1,1,5,25,219,1978,18395,171529,1601725,14956266,139629194,1303138445,
%T A005452 12157779067,113382522382,1056867697737,9843661720634,91532722388023,
%U A005452 846837132071729,7668156860181597
%N 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.
%C A005452 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.
%C A005452 The total number of inequivalent positions is 901083404981813616. - Jerry Bryan, Mar 03 2003
%D A005452 Robert G. Bryan (Jerry Bryan), postings to Cube Lovers List, Feb 04, 1995 and Oct 26, 1998.
%H A005452 Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-15.gz">Cube Lovers Archive, Part 15</a>
%H A005452 Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-16.gz">Cube Lovers Archive, Part 16</a>
%H A005452 Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-26.gz">Cube Lovers Archive, Part 26</a>
%H A005452 Tomas Rokicki, <a href="http://cube20.org/qtm">God's Number in the Quarter-Turn Metric</a>
%H A005452 Tomas Rokicki, <a href="http://cube20.org/symmetry">Symmetrical Positions</a>
%Y A005452 This is A080602 reduced by action of group of order 48. Cf. A080583, A080601, A080638.
%K A005452 nonn,fini
%O A005452 0,3
%A A005452 _N. J. A. Sloane_, Feb 25 2003
%E A005452 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