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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
1, 2, 3, 7, 9, 16, 19, 29, 33
OFFSET
1,2
FORMULA
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).
Empirical G.f.: x*(1+x-x^2+2*x^3+x^4)/((1-x)^3*(1+x)^2). [Colin Barker, Apr 12 2012]
EXAMPLE
For n=4, here is a path with 7 squares; the "x" is not visited:
1.3.
.2.4
7.5.
.6.x
CROSSREFS
Sequence in context: A109660 A236544 A343198 * A347268 A360251 A140189
KEYWORD
nonn
AUTHOR
Jon Perry, Oct 15 2002
EXTENSIONS
Edited by Dean Hickerson, Oct 25 2002
STATUS
approved