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arXiv · 1901.04647

Some Linear Recurrences Motivated by Stern's Diatomic Array

Richard P. Stanley
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Abstract

We define a triangular array closely related to Stern's diatomic array and show that for a fixed integer $r\geq 1$, the sum $u_r(n)$ of the $r$th powers of the entries in row $n$ satisfy a linear recurrence with constant coefficients. The proof technique yields a vast generalization. In certain cases we can be more explicit about the resulting linear recurrence.

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Richard P. Stanley. 2019-01-15. Some Linear Recurrences Motivated by Stern's Diatomic Array. https://arxiv.org/abs/1901.04647

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