A285875 Number of possible chess games at the end of the n-th ply starting without knights.

1, 18, 324, 6572, 132640, 3030492, 68633066, 1733220521, 43321058602, 1182486223832

Offset

0,2

Comments

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.

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

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.

Initial terms computed using the Chesspresso engine.

Links

Table of n, a(n) for n=0..9.

Chesspresso^TM.

Example

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).

Crossrefs

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

Sequence in context: A285878 A171292 A001027 * A223311 A041145 A041614

Adjacent sequences: A285872 A285873 A285874 * A285876 A285877 A285878

Keyword

nonn,hard,more,fini

Author

Sean A. Irvine, Apr 28 2017

Status

approved