MathDB

In a

9\times9

board, the squares are labeled from 11 to 99, with the first digit indicating the row and the second digit indicating the column.
One would like to paint the squares in black or white in a way that each black square is adjacent to at most one other black square and each white square is adjacent to at most one other white square. Two squares are adjacent if they share a common side.
How many ways are there to paint the board such that the squares

44

and

49

are both black?

Problem Statement