steps would be appreciated

More Practice Problems 1. Use generating function to solve the recurrence relation an = 2an-1 + 3an-2 if ao = 0 and a1 = 8. 2. A noted vexillologist tells you that 30 of the 50 U.S. state flags have blue as a background color, twelve have stripes, 26 exhibit a plant or animal, nine have both blue in the background and stripes, 23 have both blue in the background and feature a plant or animal, and three have both stripes and a plant or animal. One of the flags in this last category (California) does not have any blue in the background. How many state flags have no blue in the background, no stripes, and no plant or animal featured? 3. Find the number of solutions of the equation x ty + z + w = 17, where x, y, z, w are nonnegative integers such that a