0,2

Definition: position = position with castling and en passant information, diagram = position without castling and en passant information.

Even though the sequence may be infinite (if none of the rules for draw is ever invoked by any of the players), the sequence becomes constant from a given rank n on, since it is increasing (I conjecture - even though some positions available at the n-th move might not be available on the (1+n)-th move) and bounded, thus it has a limit. The challenge is now to find this limit (or at least nontrivial upper bounds) and the rank from which on the sequence becomes constant. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 15 2008

Bernd Schwarzkopf, ''Die ersten Z"uge'' (The First Moves), Problemkiste (No.92, April 1994, p. 142-143).

F. Labelle, Statistics on chess positions

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to number of chess games

Cf. A083276, A048987, A090051.

Cf. also A006494, A079485, A019319.

Sequence in context: A075843 A090051 A089957 this_sequence A083276 A057745 A171294

Adjacent sequences: A019316 A019317 A019318 this_sequence A019320 A019321 A019322

nonn,hard,nice

Bernd Schwarzkopf (schwarzkopf(AT)uni-duesseldorf.de)

More terms from Richard Bean (rwb(AT)eskimo.com), Jun 02 2002

a(6)-a(8) from Francois Labelle (flab(AT)cs.berkeley.edu), Jan 19 2004