%I
%S 1,2,3,7,9,16,19,29,33
%N Maximum number of black squares on an n X n chessboard (with a black square in at least one corner) that can be covered by a single path, traveling only to adjacent black squares.
%F For n odd, a(n)=(n1)^2/2+1. For n even, it is conjectured that a(n)=(n^2n+2)/2 (it is easy to show this is a lower bound).
%F Empirical G.f.: x*(1+xx^2+2*x^3+x^4)/((1x)^3*(1+x)^2). [Colin Barker, Apr 12 2012]
%e For n=4, here is a path with 7 squares; the "x" is not visited:
%e 1.3.
%e .2.4
%e 7.5.
%e .6.x
%K nonn
%O 1,2
%A _Jon Perry_, Oct 15 2002
%E Edited by _Dean Hickerson_, Oct 25 2002
