Counting terms $U_n$ of third order linear recurrences with $U_n=u^2+nv^2$
英文摘要：
Given a recurrent sequence ${\bf U}:=\{U_n\}_{n\ge 0}$ we consider the problem of counting ${\mathcal M}_U(x)$, the number of integers $n\le x$ such that $U_n=u^2+nv^2$ for some integers $u,v$. We will show that ${\mathcal M}_U(x)\ll x(\log x)^{-0.05}$ for a large class of ternary sequences. Our method uses many ingredients from the proof of Alba González and the second author that ${\mathcal M}_F(x)\ll x(\log x)^{-0.06}$, with $\bf F$ the Fibonacci sequence.
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。
