A079485 Number of chess games that end in checkmate after exactly n plies.

0, 0, 0, 0, 8, 347, 10828, 435767, 9852036, 400191963, 8790619155, 362290010907, 8361091858959, 346742245764219

Offset: 0

Author

N. J. A. Sloane, Jan 17 2003

Keywords

• nonn
• hard
• more
• nice
• fini

Comments

a(6) was computed in 1897.

Examples

			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
		

References

• H. Simpson, Chess Review, Jan-Feb 1982.

Links

• F. Labelle, Statistics on chess games
• R. P. Stanley, Extremal [Chess] Problems
• M. Willey, Iowa Chess Homepage.
• World Chess Federation, Laws of Chess: For competitions starting on or after 1 July 2014
• J. Young, Opening Tree Statistics.
• Index entries for sequences related to number of chess games

Crossrefs

Cf. A006494, A048987, A089956.

Extensions

More terms from Richard Bean, Jun 08 2003

a(9) and a(10) from François Labelle, Jan 12 2004

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

Link to Extremal [Chess] Problems of R. P. Stanley corrected by Johannes W. Meijer, Mar 01 2009

a(12) from François Labelle, Mar 04 2012

a(13) from François Labelle, Aug 15 2017