A006494 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.

1, 20, 400, 8902, 197281, 4865617, 119060679, 3195913043, 84999425906, 2439540533153, 69353270203366, 2097660204806910, 62855340727822758, 1981075507583376209

Offset: 0

Author

Ken Thompson (ken(AT)google.com)

Keywords

• nonn
• hard
• nice
• fini
• more

Comments

This sequence is A048987 plus the cumulative sum of A079485. - Richard Bean, Jun 18 2003

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

References

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

Links

• Eric Weisstein's World of Mathematics, Chess
• Index entries for sequences related to number of chess games

Crossrefs

Cf. A048987, A079485.

Extensions

a(8)-a(10) from François Labelle, Jan 22 2004

a(11) from François Labelle, Jul 25 2004, who thanks Joost de Heer for providing computer time

a(12) from François Labelle, Mar 04 2012

a(13) from François Labelle, Aug 15 2017