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Number of positions that the 3 X 3 X 3 Rubik cube puzzle can be in after exactly n moves.
3

%I #11 Jan 16 2022 12:48:14

%S 1,18,262,3502,46741,621649,8240087,109043123,1441386411,19037866206,

%T 251285929522,3314574738534,43689000394782,575342418679410

%N Number of positions that the 3 X 3 X 3 Rubik cube puzzle can be in after exactly n moves.

%C This is different from the sequence giving the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves (A080601).

%C A half-turn is considered to be a single move (rather than two moves).

%C The total number of positions is 901083404981813616.

%C Relationship with A080601: 243 = 262 - 18 - 1, 3240 = 3502 - 262, 43239 = 46741 - 3502, ...

%H Mark Longridge, <a href="http://cubeman.org/fullcube.txt">God's Algorithm Calculations for Rubik's Cube...</a>

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

%Y Cf. A080601, A080602.

%K nonn,more

%O 0,2

%A _Alexander D. Healy_, Feb 21 2003

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