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A019319
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Number of possible chess diagrams after n plies.
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4
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1, 20, 400, 5362, 71852, 815677, 9260610, 94305342, 958605819, 8866424380, 81766238574
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Definition: position = position with castling and en passant information, diagram = position without castling and en passant information.
Even though the sequence may be infinite (if none of the rules for draw is ever invoked by any of the players), the sequence becomes constant from a given rank n on, since it is increasing (I conjecture - even though some positions available at the n-th move might not be available on the (1+n)-th move) and bounded, thus it has a limit. The challenge is now to find this limit (or at least nontrivial upper bounds) and the rank from which on the sequence becomes constant. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 15 2008
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REFERENCES
| Bernd Schwarzkopf, ''Die ersten Z"uge'' (The First Moves), Problemkiste (No.92, April 1994, p. 142-143).
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LINKS
| F. Labelle, Statistics on chess positions
Eric Weisstein's World of Mathematics, Chess
Index entries for sequences related to number of chess games
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CROSSREFS
| Cf. A083276, A048987, A090051, A006494, A079485, A019319.
Sequence in context: A188759 A189698 A188988 * A083276 A057745 A189198
Adjacent sequences: A019316 A019317 A019318 * A019320 A019321 A019322
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KEYWORD
| nonn,hard,nice
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AUTHOR
| Bernd Schwarzkopf (schwarzkopf(AT)uni-duesseldorf.de)
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EXTENSIONS
| More terms from Richard Bean (rwb(AT)eskimo.com), Jun 02 2002
a(6)-a(8) from Francois Labelle (flab(AT)cs.berkeley.edu), Jan 19 2004
a(9)-a(10) from Arkadiusz Wesolowski, Jan 04 2012
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