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%I #16 Jun 07 2013 12:47:27
%S 120,6972,261224,7092774,148688232,2503611964,34779531480,
%T 406309208481,4048627642976,34778882769216,259669578902016,
%U 1695618078654976,9726900031328256,49134911067979776,218511510918189056,852888183557922816
%N Number of n-piece positions at checkers, for n=1 ... 24.
%C The total number of possible positions is a(1)+...+a(24) = 500995484682338672639.
%C However, not all of these positions are legal, i.e. reachable from the start position. - _Ralf Stephan_, Sep 18 2004
%D 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.
%D 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.
%H J. Schaeffer, <a href="/A055213/b055213.txt">Table of n, a(n) for n = 1..24</a> (complete sequence)
%H J. Schaeffer, <a href="http://www.cs.ualberta.ca/~chinook/databases/checker_positions.html">Chinook: Full sequence and more info</a>
%H J. Schaeffer, <a href="http://www.cs.ualberta.ca/~chinook/publications/">Chinook: Publications</a>
%H J. Schaeffer and R. Lake, Solving the game of checkers, in: R. Nowakowski (ed.), <a href="http://www.msri.org/publications/books/Book29/index.html">Games of No Chance (1996)</a>, p. 119-133.
%H Yngvi Bjornsson, N. Burch, Rob Lake, Joe Culberson, Paul Lu, Jonathan Schaeffer, Steve Sutphen, <a href="http://www.cs.ualberta.ca/~chinook/databases/checker_positions.html">Chinook: Total Number of Positions</a>
%e 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.
%Y A133803(n) = floor log a(n).
%K fini,full,nonn
%O 1,1
%A _Jud McCranie_, Jun 23 2000
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