论文标题
在线性复发序列的（几乎）可实现的子序列
On (almost) realizable subsequences of linearly recurrent sequences
论文作者
论文摘要
在本说明中，我们表明，如果$（u_n）_ {n \ geqslant 1} $是一个简单的线性复发序列，其最小的订单$ k $的最低复发仅涉及积极的直接系数，则具有正面术语的正数，则$（mu_ {n^s} _ {n^s} _ {整数$ m $和$ s $任何足够大的$ k！$。这扩展了Moss和Ward [斐波那契季刊60（2022），40-47]的结果，他们证明了斐波那契序列的结果。
In this note we show that if $(u_n)_{n\geqslant 1}$ is a simple linearly recurrent sequence of integers whose minimal recurrence of order $k$ involves only positive coefficients that has positive initial terms, then $(Mu_{n^s})_{n\geqslant 1}$ is the sequence of periodic point counts for some map for a suitable positive integer $M$ and $s$ any sufficiently large multiple of $k!$. This extends a result of Moss and Ward [The Fibonacci Quarterly 60 (2022), 40-47] who proved the result for the Fibonacci sequence.
