A006494 - OEIS

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

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OFFSET

0,2

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

Table of n, a(n) for n=0..13.

Eric Weisstein's World of Mathematics, Chess

Index entries for sequences related to number of chess games

CROSSREFS

Cf. A048987, A079485.

Sequence in context: A285874 A007577 A048987 * A007545 A055476 A223180

Adjacent sequences: A006491 A006492 A006493 * A006495 A006496 A006497

KEYWORD

nonn,hard,nice,fini,more