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

Author

Sean A. Irvine, Apr 28 2017

Keywords

• nonn
• hard
• more
• fini

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

• Bernhard Seybold, Chesspresso.

Crossrefs

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

Extensions

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