Irreducible polynomials over GF(2) with three prescribed coefficients

For an odd positive integer n, we determine formulas for the number of irreducible polynomials of degree n over GF(2) in which the coefficients of xn−1, xn−2 and xn−3 are specified in advance. Formulas for the number of elements in GF(2n) with the first three traces specified are also given.