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A126685 In chess, the number of checkmate dual-free proof games in n plies. 0

%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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