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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

%I #7 May 13 2019 15:16:15

%S 1,2,9,75,934,12077,159131,2101575,27762103,366611212,4838564147,

%T 63818720716,841134600018,11076115427897

%N 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.

%C 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 A half-turn is considered to be 1 move.

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

%D Robert G. Bryan (Jerry Bryan), posting to Cube Lovers List, Jul 10, 1998.

%H Alan Bawden, <a href="ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-25.gz">Cube Lovers Archive, Part 25</a>

%H Rokicki, Tomas; <a href="http://forum.cubeman.org/?q=node/view/146">God's Algorithm out to 13f*</a>

%Y This is A080601 reduced by action of group of order 48. Cf. A005452, A080602.

%K nonn,fini

%O 0,2

%A _N. J. A. Sloane_, Feb 28 2003

%E Added a(11)..a(13) _Tomas Rokicki_, Jul 25 2009