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

Offset: 0

Author

François Labelle, Mar 04 2012

Keywords

• nonn
• hard
• fini
• more

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

• F. Labelle, Statistics on chess positions
• Index entries for sequences related to number of chess games

Crossrefs

Cf. A019319, A090051, A209433.

Extensions

a(11) from François Labelle, Feb 27 2017