MathDB

The nonnegative integer

n

and

(2n + 1) \times (2n + 1)

chessboard with squares colored alternatively black and white are given. For every natural number

m

with

1 < m < 2n+1

, an

m \times m

square of the given chessboard that has more than half of its area colored in black, is called a

B

-square. If the given chessboard is a

B

-square, find in terms of

n

the total number of

B

-squares of this chessboard.

Problem Statement