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Search: id:A083276
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| A083276 |
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Number of distinct chess positions after n plies including differences due to availability and possibility of castling and en passant captures. |
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+0
5
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| 1, 20, 400, 5362, 72078, 822518, 9417681, 96400068, 988187354, 9183421888
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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LINKS
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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.]
Index entries for sequences related to number of chess games
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CROSSREFS
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Cf. A019319, A048987, A057745, A089957.
Sequence in context: A090051 A089957 A019319 this_sequence A057745 A009964 A007577
Adjacent sequences: A083273 A083274 A083275 this_sequence A083277 A083278 A083279
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KEYWORD
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hard,nonn,nice
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AUTHOR
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Richard Bean (rwb(AT)eskimo.com), Jun 02 2003
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EXTENSIONS
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a(9) from Paul Byrne (ibid(AT)carolina.rr.com), Jan 26 2004
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