# 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?

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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