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A006494
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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.
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7
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1, 20, 400, 8902, 197281, 4865617, 119060679, 3195913043, 84999425906, 2439540533153, 69353270203366, 2097660204806910, 62855340727822758, 1981075507583376209
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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James Gleick, Faster, Vintage Books, NY, 2000 (see pp. 259-261).
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LINKS
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Eric Weisstein's World of Mathematics, Chess
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CROSSREFS
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KEYWORD
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nonn,hard,nice,fini
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AUTHOR
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Ken Thompson (ken(AT)google.com)
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EXTENSIONS
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a(11) from François Labelle, Jul 25 2004, who thanks Joost de Heer for providing computer time
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STATUS
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approved
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