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number of ways of distributing $k$ candies to $n$ children

Source: Canadian Mathematical Olympiad 2006 , problem 1

January 28, 2007
combinatorics proposedcombinatorics

Problem Statement

Let f(n,k) f(n,k) be the number of ways of distributing k k candies to n n children so that each child receives at most 2 2 candies. For example f(3,7) \equal{} 0,f(3,6) \equal{} 1,f(3,4) \equal{} 6. Determine the value of f(2006,1) \plus{} f(2006,4) \plus{} \ldots \plus{} f(2006,1000) \plus{} f(2006,1003) \plus{} \ldots \plus{} f(2006,4012).
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