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Unformatted text preview: (c) Suppose we only require that each of the ﬁve people gets at least one jellybean (of some color) but that no CSE major gets more than two blue jellybeans? Now how many ways are possible? 3.4 Solve the following linear recurrences: (a) x n +1 = 3 x n2 , x 1 = 2; (b) x n +1 = 3 x n2 , x 1 = 1; 3.5 Deﬁne the usual Fibonacci numbers by: F = 0 , F 1 = 1, and F n +2 = F n +1 + F n , n ≥ 0. Prove by induction that: (a) ∑ n k =1 F 2 k = F 2 n +11; (b) F n +1 F n1 = F 2 n + (1) n . 1 3.6 Solve the second order linear recurrences: (a) y n +2 = 2 y n +1 + y n , y = 0 , y 1 = 1; (b) y n +2 = 2 y n +1y n , y = 0 , y 1 = 1 . 2...
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 Fall '07
 Graham
 Confectionery, Jelly bean, Linear Recurrences, order linear recurrences, following linear recurrences

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