cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A209080 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.

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%I A209080 #20 Feb 28 2017 02:45:59
%S A209080 1,20,400,1702,8659,49401,287740,1934794,11569093,65443733,360231372,
%T A209080 1872156836
%N A209080 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 A209080 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 A209080 F. Labelle, <a href="http://wismuth.com/chess/statistics-positions.html#shortest">Statistics on chess positions</a>
%H A209080 <a href="/index/Ch#chess">Index entries for sequences related to number of chess games</a>
%Y A209080 Cf. A019319, A090051, A209433.
%K A209080 nonn,hard,fini,more
%O A209080 0,2
%A A209080 _François Labelle_, Mar 04 2012
%E A209080 a(11) from _François Labelle_, Feb 27 2017