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Search: id:A080601
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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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+0
24
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| 1, 18, 243, 3240, 43239, 574908, 7618438, 100803036, 1332343288, 17596479795, 232248063316, 3063288809012, 40374425656248, 531653418284628
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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
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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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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]
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CROSSREFS
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Cf. A080638, A005452, A080602.
Sequence in context: A021064 A080629 A053540 this_sequence A016186 A081203 A016294
Adjacent sequences: A080598 A080599 A080600 this_sequence 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 (njas(AT)research.att.com), Feb 25 2003
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EXTENSIONS
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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
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