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%I A126685
%S A126685 0,0,0,0,0,3,51,1106,3813,47300,216420,2057581
%N A126685 In chess, the number of checkmate dual-free proof games in n plies.
%C A126685 Among all the proof game problems counted in A090051, this is the number 
               of problems ending in checkmate.
%H A126685 F. Labelle, <a href="http://www.cs.berkeley.edu/~flab/chess/statistics-positions.html#checkmate">
               Statistics on checkmate diagrams</a>.
%H A126685 Retrograde Analysis Corner, <a href="http://www.janko.at/Retros/Records/
               ShortestMate/index.htm">Shortest Mates in Proof Games</a>.
%e A126685 a(5)=3 because there are three checkmate proof games in 5 plies:
%e A126685 1. e4 e5 2. Qh5 Ke7 3. Qxe5#
%e A126685 1. e3 e5 2. Qh5 Ke7 3. Qxe5#
%e A126685 1. e4 f5 2. exf5 g5 3. Qh5#
%Y A126685 Cf. A090051, A102784.
%Y A126685 Sequence in context: A045489 A145242 A075869 this_sequence A105639 A003028 
               A069343
%Y A126685 Adjacent sequences: A126682 A126683 A126684 this_sequence A126686 A126687 
               A126688
%K A126685 hard,nonn
%O A126685 0,6
%A A126685 Francois Labelle (flab(AT)cs.berkeley.edu), Feb 13 2007

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