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# T3 - a n Problem 3 Find the number of non-negative integers...

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Problem 1: Find the generating function for the number of compositions of n with an odd number of parts, each of which is congruent to 1 (mod 3). Problem 2: Consider the set A of compositions of n in which at least one of the parts is greater than 3. (a) Find the generating function of A . (b) Let a n be the number of compositions of n in which at least one of the parts is greater than 3, find a recurrence relation for
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Unformatted text preview: a n . Problem 3: Find the number of non-negative integers less than 1,000,000 whose digits sum up to no more than 23. Problem 4: We call an n-digit number valid if it contains an even number of 0s. Let a n be the number of valid n-digit numbers. (a) Find a recurrence relation for a n . (b) Use generating functions to ﬁnd an explicit formula for a n . 1...
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