There is a board with the shape of an equilateral triangle with side n divided into triangular cells with the shape of equilateral triangles with side 1 (the figure below shows the board when n=4). Each and every triangular cell is colored either red or blue. What is the least number of cells that can be colored blue without two red cells sharing one side?
https://cdn.artofproblemsolving.com/attachments/0/1/d1f034258966b319dc87297bdb311f134497b5.png combinatoricsColoringEquilateral