Some basic line-sequential properties of polynomial line-sequences (Q2735214)

For a second-order recurrent sequence \(u_n= bu_{n-1}+ cu_{n-2}\) with integral or polynomial coefficients \(b\) and \(c\), the author discusses its properties in the vector space consisting of all these sequences. He shows that there exist two basis sequences that can generate all sequences. Moreover, with a method of translational expression, every sequence can be represented by either basis sequence. As applications, properties of some special known sequences are discussed in the paper.