A337746 Maximum number of bishops within an n X n chessboard, where each bishop has a path to an edge.

1, 4, 8, 12, 19, 28, 37, 48, 57, 72, 87

Offset: 1

Author

Nicholas Tran, Sep 17 2020

Keywords

• nonn
• hard
• more

Comments

Given an n X n chessboard, this sequence is the maximum number of bishops that can be placed on the board, such that each bishop has a free path to the edge of the board without another bishop moving.

Bishops on even and odd squares don't interfere and can be maximized separately. When n is even, the two types are equal via symmetry and thus the maximum number of bishops will be 2 * (maximum number of one type of bishop).

Links

• Nicholas Tran, Solution in ASP

Crossrefs

Cf. A337722 (knights), A335445 (rooks).