Answer to Question #21676 in Differential Equations for Vanessa

Question #21676
Express the solution to the following counting problem in terms of a difference equation, then use a generating function to solve the difference equation to give an explicit solution: Bob is threading beads onto a wire to make a decorative keyring. He has an unlimited supply of 2 cm long beads in a choice of red, orange, yellow, green, blue, or purple, as well as an unlimited supply of 1 cm long black beads. If the wire is n cm long, how many different sequences of beads are possible?
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