Coloring in Hypercube

In an N-dimensional grid the co-ordinates of a cell are denoted as X1, X2, ..., XN. Any cell with negative co-ordinate are colored white. The origin cell (the one with all zero co-ordinates) is colored as black. The color of a cell in (X1, X2, ..., XN) depends on the N cells with co-ordinates (X1-1, X2, ..., XN), (X1, X2-1, ..., XN), ...., (X1, X2, ..., XN-1). The cell is colored white if and only