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A080601
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Number of positions that the 3 X 3 X 3 Rubik cube puzzle can be in after exactly n moves.
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23
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1, 18, 243, 3240, 43239, 574908, 7618438, 100803036, 1332343288, 17596479795, 232248063316, 3063288809012, 40374425656248, 531653418284628, 6989320578825358, 91365146187124313
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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 half-turn is considered to be a single move (rather than two 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
| Robert G. Bryan (Jerry Bryan), posting to Cube Lovers List, Jul 10, 1998.
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LINKS
| Alan Bawden, Cube Lovers Archive, Part 25
Mark Longridge, God's Algorithm Calculations for Rubik's Cube...
Author?, God's Algorithm... [From Herbert Kociemba (kociemba(AT)t-online.de), Jun 24 2009]
Rokicki, Tomas; God's Algorithm out to 13f* [From Tomas Rokicki (rokicki(AT)cs.stanford.edu), Jul 25 2009]
15f* in the Face Turn Metric. [From Tomas Rokicki (rokicki(AT)gmail.com), Jul 29 2010]
God's Algorithm out to 14f* [From Tomas Rokicki (rokicki(AT)gmail.com), Jul 29 2010]
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CROSSREFS
| 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
| nonn,fini
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 25 2003
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EXTENSIONS
| Term a(11) from Jerry Bryan 2006, term a(12) from Tom Rokicki 2009 Herbert Kociemba (kociemba(AT)t-online.de), Jun 24 2009
Added a(13). Tomas Rokicki (rokicki(AT)cs.stanford.edu), Jul 25 2009
Added a(14) (from Thomas Scheunemann) and a(15) (from Morley Davidson, John Dethridge, Herbert Kociemba, and Tomas Rokicki). Tomas Rokicki (rokicki(AT)gmail.com), Jul 29 2010
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