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A080601
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Number of positions in which the 3 X 3 X 3 Rubik's cube puzzle can be after exactly n moves, where a move is either a quarter-turn or a half-turn.
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25
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1, 18, 243, 3240, 43239, 574908, 7618438, 100803036, 1332343288, 17596479795, 232248063316, 3063288809012, 40374425656248, 531653418284628, 6989320578825358, 91365146187124313
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listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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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.
The total number of positions is (8!*12!/2)*(2^12/2)*(3^8/3) = 43252003274489856000. - Jerry Bryan, Mar 03 2003
Relationship with A080583: 243 = 262 - 18 - 1, 3240 = 3502 - 262, 43239 = 46741 - 3502, ...
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REFERENCES
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Robert G. Bryan (Jerry Bryan), posting to Cube Lovers List, Jul 10, 1998.
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LINKS
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Table of n, a(n) for n=0..15.
Alan Bawden, Cube Lovers Archive, Part 25
Mark Longridge, God's Algorithm Calculations for Rubik's Cube...
Author?, God's Algorithm...
Tomas Rokicki, God's Algorithm out to 13f*
Tomas Rokicki, God's Number is 20
T. Rokiki, Twenty-two moves suffice for Rubik's Cube, Math. Intell. 32 (1) (2010) 33-40.
15f* in the Face Turn Metric. - Tomas Rokicki, Jul 29 2010
God's Algorithm out to 14f* - Tomas Rokicki, Jul 29 2010
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CROSSREFS
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Cf. A080638, A005452, A080602.
Sequence in context: A181379 A080629 A053540 * A016186 A081203 A016294
Adjacent sequences: A080598 A080599 A080600 * A080602 A080603 A080604
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KEYWORD
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nonn,fini
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AUTHOR
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N. J. A. Sloane, Feb 25 2003
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EXTENSIONS
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a(11) (from Jerry Bryan, 2006) and a(12) (from Tom Rokicki, 2009) added by Herbert Kociemba, Jun 24 2009
a(13) added by Tomas Rokicki, Jul 25 2009
a(14) (from Thomas Scheunemann) and a(15) (from Morley Davidson, John Dethridge, Herbert Kociemba, and Tomas Rokicki) added by Tomas Rokicki, Jul 29 2010
Name edited by Charles R Greathouse IV, Jan 19 2016
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STATUS
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approved
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