It is known that the generating function \(\sum^ \infty_{q=0}w^ k_ qz^ q\) of the sequence \(\{w^ k_ q\}\) of \(k\)th powers of a linear recurrence sequence \(\{w_ q\}\) is a rational function in \(z\). The present paper studies the degrees of polynomials in the numerator and denumerator of the generating function in the general case using Hadamard’s multiplication theorem and Cauchy’s residue theorem.