%I #70 Jul 05 2022 12:05:34
%S 1,20,400,8902,197281,4865609,119060324,3195901860,84998978956,
%T 2439530234167,69352859712417,2097651003696806,62854969236701747,
%U 1981066775000396239,61885021521585529237,2015099950053364471960
%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. - _François 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 Jakub Kowalski, Marek Szykuła, <a href="https://folk.idi.ntnu.no/odderik/RAI-2020/Experimental_Studies_in_General_Game_Playing-An_Experience_Report.pdf">Experimental Studies in General Game Playing: An Experience Report</a>, University of Wrocław, (Poland, 2020).
%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 Wikipedia, <a href="https://en.m.wikipedia.org/wiki/Shannon_number">Shannon number</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 _François 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
%E a(15) from _Paul Barnett_ on Jul 04 2022, value from wikipedia page "Shannon number"