|
|
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
|
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|