Using a nozzle to paint each square in a 1×n stripe, when the nozzle is aiming at the i-th square, the square is painted black, and simultaneously, its left and right neighboring square (if exists) each has an independent probability of 21 to be painted black.In the optimal strategy (i.e. achieving least possible number of painting), the expectation of number of painting to paint all the squares black, is T(n). Find the explicit formula of T(n). combinatoricsalgebraprobability