A285874 Number of possible chess games at the end of the n-th ply starting without rooks.

1, 20, 400, 8702, 188473, 4505624, 106770421, 2770746488, 71151220765, 1969755500063

Offset

0,2

Comments

Gives the number of possible chess games where both sides start without rooks. Rooks 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 A285874(n) <= A048987(n) for all n.

Initial terms computed using the Chesspresso engine.

Links

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

Bernhard Seybold, Chesspresso.

Crossrefs

Cf. A048987 (standard), A285873 (no queens), A285875 (no knights), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).

Sequence in context: A171294 A267793 A009964 * A007577 A048987 A006494

Adjacent sequences: A285871 A285872 A285873 * A285875 A285876 A285877

Keyword

nonn,hard,more,fini

Author

Sean A. Irvine, Apr 28 2017

Extensions

a(9) from Sean A. Irvine, May 04 2017

Status

approved