A083276 Number of distinct chess positions after n plies including differences due to availability and possibility of castling and en passant captures.

1, 20, 400, 5362, 72078, 822518, 9417681, 96400068, 988187354, 9183421888, 85375278064, 726155461002

Offset

0,2

Comments

This differs from A057745 at 6 ply and above because where an en passant capture would be illegal, the position is essentially the same as where an en passant capture is not available. It is two less than A057745 at 6 ply because the positions after 1. f4 e6/e5 2. Kf2 Qf6 3. f5 g5 are considered to be the same as after 1. f4 g5 2. Kf2 e6/e5 3. f5 Qf6.

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

The sequence became finite on Jul 01 2014 with the introduction of a new draw rule which is automatic (the 75-move rule). - François Labelle, Apr 02 2015

Links

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

Paul Byrne, Confirmation of a(10).

Tim Krabbe's chess blog, Item 283 [Mentions schachzahl1b_e.html]

F. Labelle, Statistics on chess positions

P. Österlund, Computation of a(11).

Reinhard Scharnagl, Schach und Zahlen [a serious approximation to the number of possible chess positions is 2.28*10^46.]

Index entries for sequences related to number of chess games

Crossrefs

Cf. A019319, A048987, A057745, A089957.

Sequence in context: A209433 A188988 A019319 * A057745 A224386 A189198

Adjacent sequences: A083273 A083274 A083275 * A083277 A083278 A083279

Keyword

hard,more,nonn,nice,fini

Author

Richard Bean, Jun 02 2003

Extensions

a(9) from Paul Byrne, Jan 26 2004

a(10) from Arkadiusz Wesolowski, Jan 04 2012

a(11) from Peter Österlund on Feb 22 2013, verified by François Labelle on Jan 08 2017

Status

approved