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A083276 Number of distinct chess positions after n plies including differences due to availability and possibility of castling and en passant captures. 4

%I

%S 1,20,400,5362,72078,822518,9417681,96400068,988187354,9183421888,

%T 85375278064

%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.

%H Tim Krabbe's chess blog, <a href="http://www.xs4all.nl/~timkr/chess2/diary.htm">Item 283</a> [Mentions schachzahl1b_e.html]

%H Author?, <a href="http://www.chessbox.de/Compu/schachzahl1b_e.html">Title?</a> [a serious approximation to the number of possible chess positions is 2.28*10^46.]

%H F. Labelle, <a href="http://wismuth.com/chess/statistics-positions.html">Statistics on chess positions</a>

%H Paul Byrne, <a href="http://talkchess.com/forum/viewtopic.php?p=414253">Confirmation of a(10)</a>.

%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,nonn,nice

%O 0,2

%A Richard Bean (rwb(AT)eskimo.com), Jun 02 2003

%E a(9) from _Paul Byrne_, Jan 26 2004

%E a(10) from _Arkadiusz Wesolowski_, Jan 04 2012

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Last modified October 30 09:35 EDT 2014. Contains 248797 sequences.