On the set of zero coefficients of a function satisfying a linear differential equation

Jason P. Bell, Stanley N. Burris, Karen Yeats

Let $K$ be a field of characteristic zero and suppose that $f:\mathbb{N}\to K$ satisfies a recurrence of the form $$f(n)=\sum _{i=1}^d{P}_i(n)f(n-i),$$ for $n$ sufficiently larg…