Geodesic
Root location for the characteristic polynomial of a Fibonacci type sequence
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 189-195 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We analyse the roots of the polynomial $x^n-px^{n-1}-qx-1$ for $p\geqslant q\geqslant 1$. This is the characteristic polynomial of the recurrence relation $F_{k,p,q}(n) = pF_{k,p,q}(n- \nobreak 1) + qF_{k,p,q}(n-k + 1) + F_{k,p,q}(n-k)$ 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.
We analyse the roots of the polynomial $x^n-px^{n-1}-qx-1$ for $p\geqslant q\geqslant 1$. This is the characteristic polynomial of the recurrence relation $F_{k,p,q}(n) = pF_{k,p,q}(n- \nobreak 1) + qF_{k,p,q}(n-k + 1) + F_{k,p,q}(n-k)$ 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.
DOI : 10.21136/CMJ.2022.0043-22
Classification : 11A63, 11B39, 11J86
Keywords: Fibonacci number; root; characteristic polynomial 
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     title = {Root location for the characteristic polynomial of a {Fibonacci} type sequence},
     journal = {Czechoslovak Mathematical Journal},
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     year = {2023},
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Du, Zhibin; da Fonseca, Carlos M. Root location for the characteristic polynomial of a Fibonacci type sequence. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 189-195. doi: 10.21136/CMJ.2022.0043-22

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