Find the number of ways to color $n \times m$ board with white and black colors such that any $2 \times 2$ square contains the same number of black and white cells.
Source: Azerbaijan IZhO TST 2021, P2
Tags: combinatorics, board coloring
Find the number of ways to color $n \times m$ board with white and black colors such that any $2 \times 2$ square contains the same number of black and white cells.