cp's OEIS Frontend

Does not include games which end in fewer than n plies.

According to the laws of chess, the "50-move rule" and "draw by 3-fold repetition" do not prevent infinite games because they require an appeal by one of the players, but the "75-move rule" introduced on Jul 01 2014 is automatic and makes chess finite. - François Labelle, Mar 30 2015

This differs from A057745 at 6 ply and above because where an en passant capture would be illegal, the position is essentially the same as where an en passant capture is not available. It is two less than A057745 at 6 ply because the positions after 1. f4 e6/e5 2. Kf2 Qf6 3. f5 g5 are considered to be the same as after 1. f4 g5 2. Kf2 e6/e5 3. f5 Qf6.

Definition: position = position with castling and en passant information, diagram = position without castling and en passant information.

The sequence became finite on Jul 01 2014 with the introduction of a new draw rule which is automatic (the 75-move rule). - François Labelle, Apr 02 2015

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.

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.

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.