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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
1, 20, 400, 5362, 72078, 822518, 9417681, 96400068, 988187354, 9183421888, 85375278064 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..10.

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

Author?, Title? [a serious approximation to the number of possible chess positions is 2.28*10^46.]

F. Labelle, Statistics on chess positions

Paul Byrne, Confirmation of a(10).

Index entries for sequences related to number of chess games


Cf. A019319, A048987, A057745, A089957.

Sequence in context: A209433 A188988 A019319 * A057745 A224386 A189198

Adjacent sequences:  A083273 A083274 A083275 * A083277 A083278 A083279




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


a(9) from Paul Byrne, Jan 26 2004

a(10) from Arkadiusz Wesolowski, Jan 04 2012



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Last modified February 27 11:57 EST 2015. Contains 255018 sequences.