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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..9.

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: A211539 A109660 A236544 * A140189 A327066 A165803

Adjacent sequences:  A075852 A075853 A075854 * A075856 A075857 A075858

KEYWORD

nonn

AUTHOR

Jon Perry, Oct 15 2002

EXTENSIONS

Edited by Dean Hickerson, Oct 25 2002

STATUS

approved

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)