%I #8 Apr 17 2022 01:01:38

%S 1,18,324,6572,132640,3030492,68633066,1733220521,43321058602,

%T 1182486223832

%N Number of possible chess games at the end of the n-th ply starting without knights.

%C Gives the number of possible chess games where both sides start without knights. Knights are still allowed to appear later in the game through promotion.

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

%C The total number of such games should be less than the total number of standard chess games, and it appears A285875(n) <= A048987(n) for all n.

%C Initial terms computed using the Chesspresso engine.

%H <a href="http://www.chesspresso.org/">Chesspresso^TM</a>.

%e a(1) = 18 because each pawn can move forward 1 or 2 squares (16 moves) and each rook can move into the square where the knight would have been (2 moves).

%Y Cf. A048987 (standard), A285873 (no queens), A285874 (no rooks), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).

%K nonn,hard,more,fini

%O 0,2

%A _Sean A. Irvine_, Apr 28 2017