MathDB

Let

n

be a positive integer and let

k

be an integer between

1

and

n

inclusive. There is a white board of

n \times n

. We do the following process. We draw

k

rectangles with integer sides lenghts and sides parallel to the ones of the

n \times n

board, and such that each rectangle covers the top-right corner of the

n \times n

board. Then, the

k

rectangles are painted of black. This process leaves a white figure in the board.
How many different white figures are possible to do with

k

rectangles that can't be done with less than

k

rectangles?
Proposed by David Torres Flores

2