login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of chess diagrams that can be obtained in exactly one way in n plies and cannot be obtained in fewer plies. This is also the number of dual-free shortest proof games in n plies.
2

%I #20 Feb 28 2017 02:45:59

%S 1,20,400,1702,8659,49401,287740,1934794,11569093,65443733,360231372,

%T 1872156836

%N Number of chess diagrams that can be obtained in exactly one way in n plies and cannot be obtained in fewer plies. This is also the number of dual-free shortest proof games in n plies.

%C Chess diagrams are chess positions without regard to whether castling or en passant capturing is possible. They are counted in A019319. A shortest proof game (SPG) is a classic type of chess problem. Most published SPGs are dual-free (have only one solution), which is why we count diagrams that are obtained in exactly one way in the minimum number of plies.

%H F. Labelle, <a href="http://wismuth.com/chess/statistics-positions.html#shortest">Statistics on chess positions</a>

%H <a href="/index/Ch#chess">Index entries for sequences related to number of chess games</a>

%Y Cf. A019319, A090051, A209433.

%K nonn,hard,fini,more

%O 0,2

%A _François Labelle_, Mar 04 2012

%E a(11) from _François Labelle_, Feb 27 2017