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A055213
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Number of n-piece positions at checkers, for n=1 ... 24.
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4
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120, 6972, 261224, 7092774, 148688232, 2503611964, 34779531480, 406309208481, 4048627642976, 34778882769216, 259669578902016, 1695618078654976, 9726900031328256, 49134911067979776, 218511510918189056, 852888183557922816
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The total number of possible positions is a(1)+...+a(24) = 500995484682338672639.
However, not all of these positions are legal, i.e. reachable from the start position. - R. Stephan, Sep 18 2004
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REFERENCES
| Jonathan Schaeffer, N. Burch, Yngvi Bjornsson, Akihiro Kishimoto, Martin Muller, Rob Lake, Paul Lu and Steve Sutphen. "Checkers Is Solved", Science, Vol. 317, September 14, 2007, pp. 1518-1522.
Jonathan Schaeffer, Yngvi Bjornsson, N. Burch, Akihiro Kishimoto, Martin Muller, Rob Lake, Paul Lu and Steve Sutphen. Solving Checkers, International Joint Conference on Artificial Intelligence (IJCAI), pp. 292-297, 2005. Distinguished Paper Prize.
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LINKS
| J. Schaeffer, Table of n, a(n) for n = 1..24 [Taken fron link below]
J. Schaeffer, Chinook: Full sequence and more info
J. Schaeffer, Chinook: Publications
J. Schaeffer and R. Lake, Solving the game of checkers, in: R. Nowakowski (ed.), Games of No Chance (1996), p. 119-133.
Yngvi Bjornsson, N. Burch, Rob Lake, Joe Culberson, Paul Lu, Jonathan Schaeffer, Steve Sutphen, Chinook: Total Number of Positions
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EXAMPLE
| n=1: A red piece can go on any of 28 squares (it can't reside on the last row) and a red king can be on any of 32 squares. Double that to include black, total of 120.
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CROSSREFS
| A133803(n) = floor log a(n).
Sequence in context: A003438 A092710 A177758 * A035190 A035815 A001785
Adjacent sequences: A055210 A055211 A055212 * A055214 A055215 A055216
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KEYWORD
| fini,nonn,full
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Jun 23 2000
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