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Abstract
From numerical experiments, D. E. Knuth conjectured that 0 < D n+4 < D n for a combinatorial sequence (Dn ) defined as the difference Dn = Rn – Ln of two definite hypergeometric sums. The conjecture implies.an identity of type Ln = |Rn |, involving the floor function. We prove Knuth's conjecture by applying Zeilberger's algorithm as well as classical hypergeometric machinery.