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Putnam 1997 B4

Source:

May 30, 2014

Putnaminequalitiesfloor functioncollege contests

Problem Statement

Let

a_{m,n}

denote the coefficient of

x^n

in the expansion

(1+x+x^2)^n

. Prove the inequality for all integers

k\ge 0

:

0\le \sum_{\ell=0}^{\left\lfloor{\frac{2k}{3}}\right\rfloor} (-1)^{\ell} a_{k-\ell,\ell}\le 1

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