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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. 2
1, 20, 400, 1702, 8659, 49401, 287740, 1934794, 11569093, 65443733, 360231372, 1872156836 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..11.

F. Labelle, Statistics on chess positions

Index entries for sequences related to number of chess games


Cf. A019319, A090051, A209433.

Sequence in context: A207372 A208017 A208559 * A090051 A089957 A267718

Adjacent sequences:  A209077 A209078 A209079 * A209081 A209082 A209083




François Labelle, Mar 04 2012


a(11) from François Labelle, Feb 27 2017



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Last modified December 10 01:59 EST 2018. Contains 318035 sequences. (Running on oeis4.)