Intended for: August 14, 2011
Timetable
 First draft entered by Alonso del Arte on May 20, 2011 ✓
 Draft reviewed by Alonso del Arte on August 12, 2011 ✓
 Draft approved by Daniel Forgues on August 12, 2011 ✓
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A035287: Number of ways to place a nonattacking white and black rook on
chessboard.

{ 4, 36, 144, 400, 900, 1764, 3136, ... }
As it happens, this sequence has a very simple formula:
n 2 (n − 1) 2 = (n (n − 1)) 2 = {(n) 2} 2 
, the product of two consecutive
square numbers, the square of
oblong numbers or the square of the
falling factorial .
This is the number of ways of placing two objects on an
grid so that they don’t share a row or a column. Now, the number of ways of placing
objects on an
grid so that they don’t share a row or a column is
, e.g.
{(n) 3} 2 = (n (n − 1) (n − 2)) 2 
for 3 objects. And then for an
grid, the number of ways of placing
objects so that they don’t share a coordinate is
which generalizes to higher dimensions...
See:
* {{( x)n}} (falling factorial function template)