n(n+1) table

We can observe a $200\times 200$ table (without a last column). This part of table we can divide on $\frac{200^2}{4}$ disjoint squares with dimensions $2\times 2$ , so in this part we can paint at most $2\cdot \frac{200^2}{4}$ cells. In last column we have 200 cells, so in this table is painted at most $\frac{200^2}{4}+200=200\cdot 101$ cells. If we paint every second column (starting at first column) we obtain requested painting and number of painted cells is 20200