2011/02/24 by Maciej Ulas, Ulas, Maciej
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Coding theory and cryptography #math.CO #math.NT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1102.5111
16 pages
arxiv created 2011/02/24 · arxiv updated 2011/02/28
Let Bn(t) be a n-th Stern polynomial and let e(n)=\opdegBn(t) be its degree. In this note we continue our study started in \citeUl of the arithmetic properties of the sequence of Stern polynomials and the sequence \e(n)\n=1∞. We also study the sequence d(n)=\opordt=0Bn(t). Among other things we prove that d(n)=ν(n), where ν(n) is the maximal power of 2 which dividies the number n. We also count the number of the solutions of the equations e(m)=i and e(m)-d(m)=i in the interval [1,2n]. We also obtain an interesting closed expression for a certain sum involving Stern polynomials.