A055213 Number of n-piece positions at checkers, for n=1 ... 24.

120, 6972, 261224, 7092774, 148688232, 2503611964, 34779531480, 406309208481, 4048627642976, 34778882769216, 259669578902016, 1695618078654976, 9726900031328256, 49134911067979776, 218511510918189056, 852888183557922816

Offset

1,1

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. - Ralf Stephan, Sep 18 2004

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.

Links

J. Schaeffer, Table of n, a(n) for n = 1..24 (complete sequence)

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

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.

Crossrefs

A133803(n) = floor log a(n).

Sequence in context: A222157 A092710 A177758 * A035190 A240934 A035815

Adjacent sequences: A055210 A055211 A055212 * A055214 A055215 A055216

Keyword

fini,full,nonn

Author

Jud McCranie, Jun 23 2000

Status

approved