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A075855 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. 1

%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)=(n-1)^2/2+1. For n even, it is conjectured that a(n)=(n^2-n+2)/2 (it is easy to show this is a lower bound).

%F Empirical G.f.: x*(1+x-x^2+2*x^3+x^4)/((1-x)^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

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Last modified January 26 08:18 EST 2020. Contains 331278 sequences. (Running on oeis4.)