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Keywords:
sequences of binary polynomials; Stern-Brocot sequence; perfect fields of characteristic 2
sequences of binary polynomials; Stern-Brocot sequence; perfect fields of characteristic 2
Summary:
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.
References:
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[2] Euler, R., Gallardo, L.H.: On explicit formulae and linear recurrent sequences. Acta Math. Univ. Comenianae, 80, 2011, 213-219, MR 2835276 | Zbl 1255.11061
[3] He, T.-X., Shiue, P.J.-S.: On sequences of numbers and polynomials defined by linear recurrence relations of order 2. Int. J. Math. Math, Sci., 2009, Art. ID 709386, 21 pp.. MR 2552555 | Zbl 1193.11014
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