%I #10 Dec 08 2017 00:45:09
%S 0,0,0,0,0,3,51,1106,3813,47300,216420,2057581,10276981,74358924
%N In chess, the number of checkmate dual-free proof games in n plies.
%C Among all the proof game problems counted in A090051, this is the number of problems ending in checkmate.
%H F. Labelle, <a href="http://www.cs.berkeley.edu/~flab/chess/statistics-positions.html#checkmate">Statistics on checkmate diagrams</a>.
%H Retrograde Analysis Corner, <a href="http://www.janko.at/Retros/Records/ShortestMate/index.htm">Shortest Mates in Proof Games</a>.
%e a(5)=3 because there are three checkmate proof games in 5 plies:
%e 1. e4 e5 2. Qh5 Ke7 3. Qxe5#
%e 1. e3 e5 2. Qh5 Ke7 3. Qxe5#
%e 1. e4 f5 2. exf5 g5 3. Qh5#
%Y Cf. A090051, A102784.
%K hard,nonn,fini
%O 0,6
%A _François Labelle_, Feb 13 2007
%E a(12)-a(13) from _François Labelle_, Dec 05 2017
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