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Number of possible chess games at the end of the n-th ply plus number of games that terminate (i.e., mate) in fewer than n plies.
7

%I #47 Oct 12 2024 15:51:10

%S 1,20,400,8902,197281,4865617,119060679,3195913043,84999425906,

%T 2439540533153,69353270203366,2097660204806910,62855340727822758,

%U 1981075507583376209

%N Number of possible chess games at the end of the n-th ply plus number of games that terminate (i.e., mate) in fewer than n plies.

%C This sequence is A048987 plus the cumulative sum of A079485. - _Richard Bean_, Jun 18 2003

%C The word "terminate" is inappropriate if only termination by checkmate is considered, since games can also end in a draw. The earliest possible draws occur by threefold or 5-fold repetition of the starting position through, e.g., twofold resp. 4-fold repetition of the moves 1.Nf3 Nf6 2.Ng1 Ng8, or an equivalent sequence. - _M. F. Hasler_, Mar 02 2022

%D James Gleick, Faster, Vintage Books, NY, 2000 (see pp. 259-261).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Chess.html">Chess</a>

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

%Y Cf. A048987, A079485.

%K nonn,hard,nice,fini,more

%O 0,2

%A Ken Thompson (ken(AT)google.com)

%E a(8)-a(10) from _François Labelle_, Jan 22 2004

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

%E a(12) from _François Labelle_, Mar 04 2012

%E a(13) from _François Labelle_, Aug 15 2017