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A337722
Maximum number of knights within an n X n chessboard, where each knight has a path off the board.
2
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.
CROSSREFS
Cf. A337746 (bishops), A335445 (rooks).
Sequence in context: A078593 A168350 A281151 * A052117 A033611 A033615
KEYWORD
nonn,hard,more
AUTHOR
Nicholas Tran, Sep 17 2020
STATUS
approved