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A048987 Number of possible chess games at the end of the n-th ply. 16


%S 1,20,400,8902,197281,4865609,119060324,3195901860,84998978956,

%T 2439530234167,69352859712417,2097651003696806,62854969236701747,

%U 1981066775000396239,61885021521585529237

%N Number of possible chess games at the end of the n-th ply.

%C Does not include games which end in fewer than n plies.

%C According to the laws of chess, the "50-move rule" and "draw by 3-fold repetition" do not prevent infinite games because they require an appeal by one of the players, but the "75-move rule" introduced on Jul 01 2014 is automatic and makes chess finite. - _Fran├žois Labelle_, Mar 30 2015

%H A. Bertilsson, <a href="https://www.chessprogramming.org/Perft">Distributed Perft Project</a> [also found a(11)]

%H James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=Km024eldY1A">How many chess games are possible?</a> (Numberphile video), 2015.

%H F. Labelle, <a href="http://www.cs.berkeley.edu/~flab/chess/statistics-games.html">Statistics on chess games</a>

%H T. Sillke, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/SEQUENCES/series014">number of legal chess positions</a>

%H R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/transparencies/iap.pdf">Extremal [Chess] Problems</a>

%H <a href="/index/Ch#chess">Index entries for sequences related to number of chess games</a>

%Y Cf. A006494, A079485, A083276, A019319, A285873 (no queens), A285874 (no rooks), A285875 (no knights), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).

%K nonn,nice,hard,more,fini

%O 0,2

%A _S. J. Edwards_

%E a(10) from _Richard Bean_, Jun 02 2003

%E a(11) from _Fran├žois Labelle_, Jul 25 2004, who thanks Joost de Heer for providing computer time

%E a(12) from _Paul Byrne_ on Oct 24 2006, verified by _S. J. Edwards_ on Apr 25 2011

%E a(13) from _Paul Byrne_ on Nov 08 2011, verified by _S. J. Edwards_ on Oct 03 2012

%E a(14) from _Richard Bean_ on Jul 24 2018, value from Peter Osterlund and Ankan Banerjee

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)