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A375762
Maximum number of knights within an n X n chessboard, where each knight has a path to an edge.
0
1, 4, 8, 14, 20, 30, 41, 55
OFFSET
1,2
COMMENTS
Each knight must be either already on an edge square, or have a path of unoccupied squares which reach an unoccupied edge square (and without any other knights moving).
EXAMPLE
For n=3, the following board, with X for each knight, is the unique solution a(3) = 8 and which cannot be 9 since the central square has no move to anywhere within the board.
XXX
X-X
XXX
For n=4, the following is a solution for a(4) = 14, with each of the 4 central knights able to make a single move to one of the unoccupied corner squares.
-XX-
XXXX
XXXX
XXXX
For n = 8, one 55 knight solution is:
XXXXXXXX
XXXXXXXX
XX-X-XXX
XX-X-XXX
-XX---XX
XXXX-XXX
XXXXXXXX
XXXXXXXX
CROSSREFS
Cf. A335445 (rooks), A337746 (bishops), A337722 (knights moving off the board).
Sequence in context: A343880 A121896 A368610 * A173290 A312686 A312687
KEYWORD
nonn,hard,more
AUTHOR
Walter Robinson, Aug 26 2024
STATUS
approved