Search: id:A019319
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%I A019319
%S A019319 1,20,400,5362,71852,815677,9260610,94305342,958605819
%N A019319 Number of possible chess diagrams after n plies.
%C A019319 Definition: position = position with castling and en passant information, 
               diagram = position without castling and en passant information.
%C A019319 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
%D A019319 Bernd Schwarzkopf, ''Die ersten Z"uge'' (The First Moves), Problemkiste 
               (No.92, April 1994, p. 142-143).
%H A019319 F. Labelle, <a href="http://www.cs.berkeley.edu/~flab/chess/statistics-positions.html">
               Statistics on chess positions</a>
%H A019319 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Chess.html">Link to a section of The World of Mathematics.</a>
%H A019319 <a href="Sindx_Ch.html#chess">Index entries for sequences related to 
               number of chess games</a>
%Y A019319 Cf. A083276, A048987, A090051.
%Y A019319 Cf. also A006494, A079485, A019319.
%Y A019319 Sequence in context: A075843 A090051 A089957 this_sequence A083276 A057745 
               A009964
%Y A019319 Adjacent sequences: A019316 A019317 A019318 this_sequence A019320 A019321 
               A019322
%K A019319 nonn,hard,nice
%O A019319 0,2
%A A019319 Bernd Schwarzkopf (schwarzkopf(AT)uni-duesseldorf.de)
%E A019319 More terms from Richard Bean (rwb(AT)eskimo.com), Jun 02 2002
%E A019319 a(6)-a(8) from Francois Labelle (flab(AT)cs.berkeley.edu), Jan 19 2004

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