Unformatted text preview: + x 2 + x 3 + x 4 = 30 , x 1 ≥ 1 , x 2 ≥ 2 , x 3 ≥ 3 , x 4 ≥ 4? [3] (b) How many nonnegative integer solutions are there to x 1 + x 2 + x 3 + x 4 = 30 , 1 ≤ x 1 ≤ 10 , 2 ≤ x 2 ≤ 11? [3] 4. What is the generating function for the number of partitions of n ∈ N into summands (orders are ignored) that (a) cannot occur more than 11 times? [2] (b) cannot exceed 20 and cannot occur more than 11 times? [2] 5. Use characteristic polynomials to solve the recurrence relation a n =3 a n1 +10 a n2 , n ≥ 2, with initial conditions a = 1 and a 1 = 4. [5]...
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 Spring '11
 HuangJing
 Math, Characteristic polynomial, Recurrence relation, Generating function, nonnegative integer solutions, integer solutions, ﬁrst ﬁve terms

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