Palindromic Polynomial

Palindromic Polynomial

A polynomial is palindromic, if the sequence of its coefficients are a palindrome.

Let

be a polynomial of degree n, then P is palindromic if a_i = a_{n − i} for i = 0, 1, ... n.

Similarly, P is called antipalindromic if a_i = −a_{n − i} for i = 0, 1, ... n. It follows from the definition that if P is of even degree (so has odd number of terms in the polynomial), then it can only be antipalindromic when the 'middle' term is 0, i.e. a_i = −a_n, where n = 2i.