A285876 Number of possible chess games at the end of the n-th ply starting without bishops.

1, 22, 484, 11248, 260904, 6434922, 158069690, 4126252938, 107097735673, 2940365284820

Offset

0,2

Comments

Gives the number of possible chess games where both sides start without bishops.

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

The initial terms exceed the corresponding terms in A048987, but this should eventually reverse and we should have A285876(n) <= A048987(n) for large enough n.

Initial terms computed using the Chesspresso engine.

Links

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

Chesspresso^TM.

Example

a(1) = 22 because we have the standard 20 opening moves, plus the queen and king can each move into the squares that would normally contain the bishops.

Crossrefs

Cf. A048987 (standard), A285873 (no queens), A285874 (no rooks), A285875 (no knights), A285877 (no pawns), A285878 (pawns and king).

Sequence in context: A223970 A171296 A009966 * A041221 A041926 A230350

Adjacent sequences: A285873 A285874 A285875 * A285877 A285878 A285879

Keyword

nonn,hard,more,fini

Author

Sean A. Irvine, Apr 28 2017

Status

approved