Hilbert Coefficients of Quadratic Algebras

If R = k[x1,...,xn]/I is a graded artinian algebra, then the length of k[x1,...,xn]/Is becomes a polynomial in s of degree n for large s. If we write this polynomial in the form ∑0<=i<=n (−1)i ei (s+n−i−1 choose n−i), then the ei's are called Hilbert coefficients of I. We will study lengths and Hilbert coefficients of some classes of quadratic algebras.