cp's OEIS Frontend

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

Even though the sequence may be infinite (if none of the rules for draw is ever invoked by any of the players), the sequence becomes constant from a given rank n on, since it is increasing (I conjecture - even though some positions available at the n-th move might not be available on the (1+n)-th move) and bounded, thus it has a limit. The challenge is now to find this limit (or at least nontrivial upper bounds) and the rank from which on the sequence becomes constant. - M. F. Hasler, Feb 15 2008

The sequence became finite on Jul 01 2014 with the introduction of a new draw rule which is automatic (the 75-move rule). About Hasler's second challenge, a chess problem by L. Ceriani and K. Fabel shows that at least one position is visited for the first time at ply 366. - François Labelle, Apr 01 2015

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

The positions are taken from the sets that are counted in A083276.

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.

Among all the proof game problems counted in A090051, this is the number of problems where all the surviving pieces are apparently on their start squares.

Among all the proof game problems counted in A090051, this is the number of problems ending in checkmate.