Geodesic
On a binary recurrent sequence of polynomials
Communications in Mathematics, Tome 22 (2014) no. 2, pp. 151-157
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In this paper, we study the properties of the sequence of polynomials given by $g_0=0,~g_1=1$, $g_{n+1}=g_n+\Delta g_{n-1}$ for $n\ge 1$, where $\Delta \in {\mathbb F}_q[t]$ is non-constant and the characteristic of ${\mathbb F}_q$ is $2$. This complements some results from R. Euler, L.H. Gallardo: On explicit formulae and linear recurrent sequences, Acta Math. Univ. Comenianae, 80 (2011) 213-219.
In this paper, we study the properties of the sequence of polynomials given by $g_0=0,~g_1=1$, $g_{n+1}=g_n+\Delta g_{n-1}$ for $n\ge 1$, where $\Delta \in {\mathbb F}_q[t]$ is non-constant and the characteristic of ${\mathbb F}_q$ is $2$. This complements some results from R. Euler, L.H. Gallardo: On explicit formulae and linear recurrent sequences, Acta Math. Univ. Comenianae, 80 (2011) 213-219.
Classification : 11B39, 11T06, 11T55
Keywords: sequences of binary polynomials; Stern-Brocot sequence; perfect fields of characteristic 2 
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Euler, Reinhardt; Gallardo, Luis H.; Luca, Florian. On a binary recurrent sequence of polynomials. Communications in Mathematics, Tome 22 (2014) no. 2, pp. 151-157. http://geodesic.mathdoc.fr/item/COMIM_2014_22_2_a3/

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