A Proof of a Conjecture of Knuth
Paule, Peter; Paule, Peter; Institut für Mathematik, RISC, J. Kepler Universitat Linz
Журнал:
Experimental Mathematics
Дата:
1996
Аннотация:
From numerical experiments, D. E. Knuth conjectured that 0 < D <sub>n+4</sub> < D <sub>n</sub> for a combinatorial sequence (D<sub>n</sub> ) defined as the difference D<sub>n</sub> = R<sub>n</sub> – L<sub>n</sub> of two definite hypergeometric sums. The conjecture implies.an identity of type L<sub>n</sub> = |R<sub>n</sub> |, involving the floor function. We prove Knuth's conjecture by applying Zeilberger's algorithm as well as classical hypergeometric machinery.
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