A285873 Number of possible chess games at the end of the n-th ply starting without queens.

1, 21, 441, 9872, 220447, 5247292, 124278971, 3113440755, 77520962327, 2024021927610

Offset

0,2

Comments

Gives the number of possible chess games where both sides start without queens. Queens 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 A285873(n) <= A048987(n) for n >= 7.

Initial terms computed using the Chesspresso engine.

Links

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

Chesspresso^TM.

Example

a(1) = 21 because there are 20 usual opening moves plus the additional move of moving the king into the vacant square where the queen would usually be.

Crossrefs

Cf. A048987 (standard), A285874 (no rooks), A285875 (no knights), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).

Sequence in context: A167255 A171295 A009965 * A189433 A041842 A215152

Adjacent sequences: A285870 A285871 A285872 * A285874 A285875 A285876

Keyword

nonn,hard,more,fini

Author

Sean A. Irvine, Apr 28 2017

Status

approved