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arXiv · 1610.07199

On the general solution of the Heideman-Hogan family of recurrences

Andrew N. W. Hone·Chloe Ward
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Abstract

We consider a family of nonlinear rational recurrences of odd order which was introduced by Heideman and Hogan. All of these recurrences have the Laurent property, implying that for a particular choice of initial data (all initial values set to 1) they generate an integer sequence. For these particular sequences, Heideman and Hogan gave a direct proof of integrality by showing that the terms of the sequence also satisfy a linear recurrence relation with constant coefficients. Here we present an analogous result for the general solution of each of these recurrences.

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Andrew N. W. Hone, Chloe Ward. 2016-10-23. On the general solution of the Heideman-Hogan family of recurrences. https://arxiv.org/abs/1610.07199

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