

A019319


Number of possible chess diagrams after n plies.


6



1, 20, 400, 5362, 71852, 815677, 9260610, 94305342, 958605819, 8866424380, 81766238574, 692390232505
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OFFSET

0,2


COMMENTS

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 nth 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 75move 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


REFERENCES

Bernd Schwarzkopf, Die ersten Züge (The First Moves), Problemkiste (No. 92, April 1994, p. 142143).


LINKS

Table of n, a(n) for n=0..11.
L. Ceriani, K. Fabel, Chess problem: Nonunique 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


CROSSREFS

Cf. A083276, A048987, A090051, A006494, A079485, A019319.
Sequence in context: A189698 A209433 A188988 * A083276 A057745 A224386
Adjacent sequences: A019316 A019317 A019318 * A019320 A019321 A019322


KEYWORD

nonn,hard,nice,fini


AUTHOR

Bernd Schwarzkopf (schwarzkopf(AT)uniduesseldorf.de)


EXTENSIONS

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


STATUS

approved



