Stern polynomials☆
Stern polynomials B k ( t ) , k ⩾ 0 , t ∈ R , are introduced in the following way: B 0 ( t ) = 0 , B 1 ( t ) = 1 , B 2 n ( t ) = t B n ( t ) , and B 2 n + 1 ( t ) = B n + 1 ( t ) + B n ( t ) .
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Sep 24, 2019 · Abstract:Let B_{n}(t) be the nth Stern polynomial, i.e., the nth term of the sequence defined recursively as B_{0}(t)=0, B_{1}(t)=1 and ...
Abstract. Stern polynomials Bk(t), k ≥ 0, t ∈ R, are introduced in the following way: B0(t) = 0, B1(t) = 1, B2n(t) = tBn(t), and B2n+1(t) = Bn+1(t) + Bn(t).
Stern polynomials and double-limit continued fractions. Acta Arith., 140:19--134, 2009. GG C. Giuli and R. Giuli. A primer on Stern's diatomic sequence ...
Key words: Stern (diatomic) sequence, Stern polynomials, hyperbinary representa- tion, standard Gray code, non-adjacent form. 1 Introduction. Stern sequence ...
In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role ...
We shall use the notion of Stern polynomials B n , introduced by Klavžar, Milutinović and Petr [1], i.e. B 1 = 1, B 2n (x) = xB n (x), B 2n+1 = B n + B n+1.
Aug 27, 2021 · The Stern polynomial is a polynomial extension of the well-studied Stern diatomic sequence, and has itself has been investigated in some depth.
May 14, 2015 · Using these polynomial sequences, we derive two different characterizations of all hyperbinary expansions of an integer n≥1 n ≥ 1 . Furthermore, ...
Stern polynomials B"k(t), k>=0, t@?R, are introduced in the following way: B"0(t)=0, B"1(t)=1, B"2"n(t)=tB"n(t), and B"2"n"+"1(t)=B"n"+"1(t)+B"n(t).