Czechoslovak Mathematical Journal, Vol. 73, No. 1, pp. 189-195, 2023
Root location for the characteristic polynomial of a Fibonacci type sequence
Zhibin Du, Carlos M. da Fonseca
Received February 5, 2022. Published online November 4, 2022.
Abstract: We analyse the roots of the polynomial $x^n-px^{n-1}-qx-1$ for $p\geqslant q\geqslant1$. 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 $n \geqslant k$, which includes the relations of several particular sequences recently defined. In the end, a matricial representation for such a recurrence relation is provided.
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Affiliations: Zhibin Du, School of Software, South China Normal University, Foshan, Guangdong 528225, P. R. China, e-mail: zhibindu@126.com, Carlos M. da Fonseca (corresponding author), Kuwait College of Science and Technology, P.O. Box 27235, Safat 13133, Kuwait; Chair of Computational Mathematics, University of Deusto, 48007 Bilbao, Spain, e-mail: c.dafonseca@kcst.edu.kw
