A209080 - OEIS

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.

1, 20, 400, 1702, 8659, 49401, 287740, 1934794, 11569093, 65443733, 360231372, 1872156836

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

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.

LINKS

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

CROSSREFS

Cf. A019319, A090051, A209433.

Sequence in context: A207372 A208017 A208559 * A090051 A089957 A267718

Adjacent sequences: A209077 A209078 A209079 * A209081 A209082 A209083

KEYWORD

nonn,hard,fini,more

AUTHOR

François Labelle, Mar 04 2012

EXTENSIONS

a(11) from François Labelle, Feb 27 2017

STATUS

approved