Polynomials Defined by a Second-Order Recurrence, Interlacing Zeros, and Gray Codes
Clark H. Kimberling · The Fibonacci Quarterly · 2010
A sequence of polynomials is defined by the recurrence Pn+1 = (Pn + c − a)2 − c, with P0 = x − c. Conditions are found for interlacing zeros among these polynomials, and an association between zeros and Gray codes is described. If c = a = 2, the polynomials are closely related to Chebyshev polynomials of the first kind.