We note that by Corollary 1,
resembles a vandermonde determinant. The major difference is the change
in structure at the diagonal. Using elementary row and column operations
on , we arrive at the equivalent m-1 by m-1 determinant
times the factor . Here ,
, and . Note that a+b+c=0. We also
record that .
Using the elementary fact that determinants of matrices of this shape
form a second order linear recurrence , where k is the size
of the matrix, we find . The associated
polynomial is , since a+b+c=0.
The closed form of this recurrence is therefore ,
and from the initial conditions and the result follows.
