%I A055213
%S A055213 120,6972,261224,7092774,148688232,2503611964,34779531480,406309208481,
%T A055213 4048627642976,34778882769216,259669578902016,1695618078654976,
%U A055213 9726900031328256,49134911067979776,218511510918189056,852888183557922816
%N A055213 Number of n-piece positions at checkers, for n=1 ... 24.
%C A055213 The total number of possible positions is a(1)+...+a(24) = 500995484682338672639.
%C A055213 However, not all of these positions are legal, i.e. reachable from the 
               start position. - R. Stephan, Sep 18 2004
%D A055213 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 A055213 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 A055213 J. Schaeffer, <a href="b055213.txt">Table of n, a(n) for n = 1..24</a> 
               [Taken fron link below]
%H A055213 J. Schaeffer, <a href="http://www.cs.ualberta.ca/~chinook/databases/checker_positions.html">
               Chinook: Full sequence and more info</a>
%H A055213 J. Schaeffer, <a href="http://www.cs.ualberta.ca/~chinook/publications/
               ">Chinook: Publications</a>
%H A055213 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 A055213 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 A055213 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 A055213 A133803(n) = floor log a(n).
%Y A055213 Sequence in context: A061541 A003438 A092710 this_sequence A035190 A035815 
               A001785
%Y A055213 Adjacent sequences: A055210 A055211 A055212 this_sequence A055214 A055215 
               A055216
%K A055213 fini,nonn,full
%O A055213 1,1
%A A055213 Jud McCranie (j.mccranie(AT)comcast.net), Jun 23 2000