MathDB

A quarter of an checkered plane is given, infinite to the right and up. All its rows and columns are numbered starting from

0

. All cells with coordinates

(2n, n)

, were cut out from this figure, starting from

n = 1

. In each of the remaining cells they wrote a number, the number of paths from the corner cell to this one (you can only walk up and to the right and you cannot pass through the removed cells). Prove that for each removed cell the numbers to the left and below it differ by exactly

2

Problem Statement