MathNet 2009-part-01 — 175 problems (EN–VI) Question 104

Given an $m \times n$ grid with squares coloured either black or white, we say that a black square in the grid is stranded if there is some square to its left in the same row that is white and there is some square above it in the same column that is white (see Figure).

A $4 \times 5$ grid with no stranded black squares

Find a closed formula for the number of $2 \times n$ grids with no stranded black squares.