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%I #10 May 24 2016 11:37:18
%S 668,1964,2434,3248,5152,8400
%N One player's total legal chess moves by piece type on standard chessboard.
%C The terms are given in order of increasing numbers of total moves for the six piece types; that is, a(1) Pawn, a(2) Knight, a(3) King, a(4) Bishop, a(5) Rook and a(6) Queen.
%C The sum of these six terms is 21866, the total number of moves available to White or to Black. Hence 43732 moves, the answer to a question raised in the link below, are available to both players.
%C Notes: (1) Capturing, for example, a Knight on a particular square counts as a different move from capturing, for example, a Rook on the same square.
%C (2) Moving a piece to a square without capturing is counted separately from captures by the piece on that square.
%C (3) The two castling moves are counted as King moves only.
%C (4) The 14 en passant captures are included in the Pawn moves.
%C (5) Two-square initial Pawn moves are included.
%C (6) Pawn promotion on a particular square to a Bishop, for example, counts as a different move from promotion to a Queen on the same square.
%C (7) Pieces of the same type and color are considered indistinguishable.
%C (8) Moves causing check, discovered check, double check, checkmate, or stalemate are not distinguished from other moves.
%C Valid boards and moves require (these two somewhat subtle realizations):
%C (9) A King cannot capture Pawns on their original squares when they would be attacking the King; this would require the King to have made an illegal move earlier by walking into check.
%C (10) A King cannot diagonally capture Bishops on their home corner squares - again this would require the King to have made an illegal move earlier. However, a King can diagonally capture Bishops on the other two corners as the Bishop can be in position *after* the King is - via Pawn promotion in this case.
%D Inspired by a question posed by Tim Krabbé.
%H T. Krabbé, <a href="http://www.xs4all.nl/~timkr/chess2/diary_6.htm">Open Chess Diary, Item 105, Mar 29 2001: Never in a trillion</a>
%F a(6) = a(4) + a(5) (Queen moves equal sum of Bishop and Rook moves). Generalizing all terms for n X n chessboards other than 8 x 8 requires defining how many pieces and how many types of pieces are originally on the board and/or can be promoted to, especially because of the way captures are counted.
%Y Cf. A035005 - A035008, A033586 (count the moves per piece type differently).
%K fini,full,nonn
%O 1,1
%A _Rick L. Shepherd_, Feb 25 2002
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