Paint It Black—A Combinatorial Yawp

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We begin by solving a problem posed from the Monthly. Show n Σ r=0 (−1)r(n r)(2n – 2r n – 1) = 0. We prove this combinatorially by pairing up objects that have an odd value of r with objects that have an even value of r. The proof, and its generalizations, lead to many new and interesting identities.

Document Type: Short Communication

Publication date: February 1, 2008

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