Final answer:
To find the number of tilings for a 2xn strip, we can use a recurrence equation. The equation is Tn = Tn-1 + Tn-2, with initial conditions T0 = 1 and T1 = 1. This can be solved using the Fibonacci sequence.
Step-by-step explanation:
To find a formula for the number of tilings, we can consider the first tile that is placed in the strip. There are two possible cases:
1. If the first tile is a 2x2 square or an L-shaped tile, then the remaining strip can be tiled in Tn-2 ways (since it reduces the width of the strip by 2).
2. If the first tile is a 1x1 orange tile, then the remaining strip can be tiled in Tn-1 ways (since it reduces the width of the strip by 1).
Therefore, the recurrence equation for Tn is Tn = Tn-1 + Tn-2 for n ≥ 2, with initial conditions T0 = 1 and T1 = 1. Using this recurrence, we can solve for Tn using the Fibonacci sequence.