A337722 Maximum number of knights within an n X n chessboard, where each knight has a path off the board.

1, 4, 9, 16, 24, 34, 44, 58, 73

Offset

1,2

Comments

Given an n X n chessboard, this sequence is the maximum number of knights that can be placed on the board, such that each knight has a free path to jump "off" the board without another knight moving.

An example for a(3):

XXX

XXX

XXX

Here, all knights can jump off the board via knight movement. The middle knight is not blocked by any pieces.

An example for a(5):

XXXXX

XXXXX

XX-XX

XXXXX

XXXXX

Here, a knight can occupy all spaces except the central space, where a knight would not be able to jump off the board and would not be able to jump to another free square.

Links

Table of n, a(n) for n=1..9.

Nicholas Tran, Solution in ASP

Crossrefs

Cf. A337746 (bishops), A335445 (rooks).

Sequence in context: A078593 A168350 A281151 * A052117 A033611 A033615

Adjacent sequences: A337719 A337720 A337721 * A337723 A337724 A337725

Keyword

nonn,hard,more

Author

Nicholas Tran, Sep 17 2020

Status

approved