Generalized Horadam Polynomials and Numbers

Abstract

We consider the polynomials hn,m(x) (m ≥ 2) and the numbers hn,m (x = 1), which are the generalized Horadam polynomials and the generalized Horadam numbers, respectively. We also consider the polynomials h(s)n,m(x)- convolutions of the polynomials hn,m(x), and the sequence of numbers h(s)n,m- convolutions of the numbers hn,m, where s ≥ 0.

Keywords

• generalized horadam polynomials and numbers
• convolution
• recurrence relation
• explicit representation
• generating function
• primary 11b83
• secondary 11b37
• 11b39