A209080 -id:A209080 - cp's OEIS frontend

A090051 Number of chess diagrams that can be obtained in exactly one way in n plies. This is also the number of dual-free proof games in n plies.

1, 20, 400, 1862, 9373, 51323, 298821, 1965313, 11759158, 66434263, 365037821, 1895313862

Offset: 0

François Labelle, Jan 19 2004

Chess diagrams are chess positions without regard to whether castling or en passant capturing is possible. They are counted in A019319. A proof game is a classic type of chess problem.

Cf. A019319, A089957, A209080.

a(9)-a(10) from Arkadiusz Wesolowski, Jan 04 2012

a(11) from François Labelle, Jan 16 2017

A209433 Number of chess diagrams that can be obtained in n plies, but not in fewer plies.

Original entry on oeis.org

1, 20, 400, 5202, 69731, 766337, 8708079, 86540204, 880526165, 7996545696, 73802185449, 616052245142

Offset: 0

François Labelle, Mar 08 2012

Chess diagrams are chess positions without regard to whether castling or en passant capturing is possible. The condition that the diagram cannot be obtained in fewer than n plies means that each legal chess diagram is counted exactly once in this sequence, indexed by the length of the shortest game(s) to reach it. Therefore, this sequence is finite and its sum equals the number of legal chess diagrams, estimated to be between 10^43 and 10^47.

Cf. A019319, A209080.

a(11) from François Labelle, Feb 27 2017

cp's OEIS Frontend

A090051 Number of chess diagrams that can be obtained in exactly one way in n plies. This is also the number of dual-free proof games in n plies.

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