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1996 A proof of a conjecture of Knuth
Peter Paule
Experiment. Math. 5(2): 83-89 (1996).

Abstract

From numerical experiments, D. E. Knuth conjectured that $0<D_{n+4}<D_n$ for a combinatorial sequence $(D_n)$ defined as the difference $D_n = R_n-L_n$ of two definite hypergeometric sums. The conjecture implies an identity of type $L_n= \lfloor R_n \rfloor$, involving the floor function. We prove Knuth's conjecture by applying Zeilberger's algorithm as well as classical hypergeometric machinery.

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Peter Paule. "A proof of a conjecture of Knuth." Experiment. Math. 5 (2) 83 - 89, 1996.

Information

Published: 1996
First available in Project Euclid: 13 March 2003

zbMATH: 0984.33009
MathSciNet: MR1418955

Subjects:
Primary: 33C20
Secondary: 05A10 , 05A19 , 11B65 , 33C05

Rights: Copyright © 1996 A K Peters, Ltd.

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Vol.5 • No. 2 • 1996
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