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追随 Richard Stanley 的脚步：与广义 Stern 二原子阵列相关的生成函数的自动生成

Automated Generation of Generating Functions Related to Generalized Stern's Diatomic Arrays in the footsteps of Richard Stanley

Shalosh B. Ekhad, Doron Zeilberger

备注：
18 pages; Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and this arxiv. Accompanied by two Maple packages and numerous input and output files available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/stern.html This version corrects the values at the top of p.3. We thank Guoce Xin for pointing out that the old values were wrong
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AI总结：

本文提出并实现了基于符号动态规划的 Maple 算法，用于自动生成广义 Stern 阵列的生成函数，并将其推广到由常系数线性递推序列定义的更一般阵列。

摘要：

利用符号动态规划，我们描述了若干算法，这些算法已在 Maple 中完整实现，用于自动生成 Richard Stanley 在研究广义 Stern 阵列时引入的生成函数。我们进一步将其推广到由满足常系数线性递推的一般序列所定义的阵列，而不仅限于 Fibonacci 序列和 k-bonacci 序列。

英文摘要：

Using Symbolic Dynamic Programming we describe algorithms, fully implemented in Maple, for automatically generating generating functions introduced by Richard Stanley in his study of generalized Stern arrays, generalized even further, to arrays defined in terms of general sequences satisfying linear recurrences with constant coefficients, rather than just the Fibonacci and k-bonacci sequences

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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