[seqfan] Maximum-area farm on a square grid

[Allan Wechsler]

On an infinite chessboard, you are allowed to mark N cells, with the aim of
enclosing an area of maximal size. If you are allowed to mark 8 cells, for
example, then I think the best you can do is to enclose 5 cells.

(By "enclose", I mean that you can't escape from an interior cell to the
outside world by a path consisting of orthogonal unit moves that never
visit a marked cell.)

With less than 4 marks, you can't enclose *any* cells, so I think this
function has the first few values A(1) = A(2) = A(3) = 0, A(4) = A(5) = 1,
A(6) = 2, A(7) = 3, A(8) = 5. I am not completely certain, but I *think *A(9)
= 6 and A(10) = 8. If these values are correct then I don't think the
sequence is in OEIS yet, which surprises me because it seems like an
obvious problem.

Obviously we expect roughly quadratic growth here. A011864 has the right
first few values but if that's the right formula I'll be mighty surprised!