Z. Du, C.M. da Fonseca (2023) Root location for the characteristic polynomial of a Fibonacci type sequence, Czechoslovak Mathematical Journal, Vol. 73, pp. 189-195, 10.21136/CMJ.2022.0043-22
Abstract. We analyse the roots of the polynomial \(x^n-px^{n-1}-qx-1\) for \(p\ge q\ge1\). This is the characteristic polynomial of the recurrence relation
F_{k,p,q}(n)=pF_{k,p,q}(n-1)+qF_{k,p,q}(n-k+1)+F_{k,p,q}(n-k) for \(n\ge k\), which includes the relations of several particular sequences recently defined. In the end, a matricial representation for such a recurrence relation is provided.