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A019319 Number of possible chess diagrams after n plies. 6
1, 20, 400, 5362, 71852, 815677, 9260610, 94305342, 958605819, 8866424380, 81766238574, 692390232505 (list; graph; refs; listen; history; text; internal format)



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, Feb 15 2008

The sequence became finite on Jul 01 2014 with the introduction of a new draw rule which is automatic (the 75-move rule). About Hasler's second challenge, a chess problem by L. Ceriani and K. Fabel shows that at least one position is visited for the first time at ply 366. - François Labelle, Apr 01 2015


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


Table of n, a(n) for n=0..11.

L. Ceriani, K. Fabel, Chess problem: Non-unique proof game in 183 moves, Am Rande des Schachbretts, 1947

F. Labelle, Statistics on chess positions

Eric Weisstein's World of Mathematics, Chess

Index entries for sequences related to number of chess games


Cf. A083276, A048987, A090051, A006494, A079485, A019319.

Sequence in context: A189698 A209433 A188988 * A083276 A057745 A224386

Adjacent sequences:  A019316 A019317 A019318 * A019320 A019321 A019322




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


More terms from Richard Bean, Jun 02 2002

a(6)-a(8) from François Labelle, Jan 19 2004

a(9)-a(10) from Arkadiusz Wesolowski, Jan 04 2012

a(11) from François Labelle, Jan 16 2017



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Last modified November 28 21:30 EST 2021. Contains 349415 sequences. (Running on oeis4.)