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%I #44 Mar 12 2022 22:43:15
%S 0,0,0,0,8,347,10828,435767,9852036,400191963,8790619155,362290010907,
%T 8361091858959,346742245764219
%N Number of chess games that end in checkmate after exactly n plies.
%C a(6) was computed in 1897.
%D H. Simpson, Chess Review, Jan-Feb 1982.
%H F. Labelle, <a href="http://www.cs.berkeley.edu/~flab/chess/statistics-games.html">Statistics on chess games</a>
%H R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/transparencies/iap.pdf">Extremal [Chess] Problems</a>
%H M. Willey, <a href="http://members.tripod.com/~wwx2/chess.html">Iowa Chess Homepage</a>.
%H World Chess Federation, <a href="https://www.fide.com/fide/handbook.html?id=171&view=article">Laws of Chess: For competitions starting on or after 1 July 2014</a>
%H J. Young, <a href="http://groups.google.com/groups?selm=6bd1k1%24nkp%40ultra0.rdrc.rpi.edu">Opening Tree Statistics</a>.
%H <a href="/index/Ch#chess">Index entries for sequences related to number of chess games</a>
%e a(n) = 0 for n < 4 and a(4) = 8, because the earliest checkmate can occur at move 2, e.g., with 1.f3 e5, 2.g4 Qh4#. The 8 = 2*2*2 possibilities counted in a(4) all correspond to essentially the same mate, with (1) the alternative 1.f4, (2) the alternative 1...e6, (3) inversed order of white's moves. - _M. F. Hasler_, Mar 03 2022
%Y Cf. A006494, A048987, A089956.
%K nonn,hard,more,nice,fini
%O 0,5
%A _N. J. A. Sloane_, Jan 17 2003
%E More terms from _Richard Bean_, Jun 08 2003
%E a(9) and a(10) from _François Labelle_, Jan 12 2004
%E a(11) from _François Labelle_, Jul 25 2004, who thanks Joost de Heer for providing computer time.
%E Link to Extremal [Chess] Problems of R. P. Stanley corrected by _Johannes W. Meijer_, Mar 01 2009
%E a(12) from _François Labelle_, Mar 04 2012
%E a(13) from _François Labelle_, Aug 15 2017
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