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%I #50 Mar 09 2021 04:14:40
%S 1,20,400,5362,72078,822518,9417681,96400068,988187354,9183421888,
%T 85375278064,726155461002
%N Number of distinct chess positions after n plies including differences due to availability and possibility of castling and en passant captures.
%C 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.
%C Definition: position = position with castling and en passant information, diagram = position without castling and en passant information.
%C 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
%H Paul Byrne, <a href="http://talkchess.com/forum/viewtopic.php?p=414253">Confirmation of a(10)</a>.
%H Tim Krabbe's chess blog, <a href="http://www.xs4all.nl/~timkr/chess2/diary.htm">Item 283</a> [Mentions schachzahl1b_e.html]
%H F. Labelle, <a href="http://wismuth.com/chess/statistics-positions.html">Statistics on chess positions</a>
%H P. Österlund, <a href="http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=508645&t=41032">Computation of a(11)</a>.
%H Reinhard Scharnagl, <a href="https://web.archive.org/web/20160419072050/http://www.10x8.net/chess/Zahlen.html">Schach und Zahlen</a> [a serious approximation to the number of possible chess positions is 2.28*10^46.]
%H <a href="/index/Ch#chess">Index entries for sequences related to number of chess games</a>
%Y Cf. A019319, A048987, A057745, A089957.
%K hard,more,nonn,nice,fini
%O 0,2
%A _Richard Bean_, Jun 02 2003
%E a(9) from _Paul Byrne_, Jan 26 2004
%E a(10) from _Arkadiusz Wesolowski_, Jan 04 2012
%E a(11) from Peter Österlund on Feb 22 2013, verified by _François Labelle_ on Jan 08 2017
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