  This is the second paper in a series of three papers. In the first paper of
the series, "Artinian Gorenstein algebras with linear resolutions",
(arXiv:1306.2523, J. of Algebra, to appear) we prove that it is possible to
give the minimal resolution of the rings from the title in terms of the
coefficients of the corresponding Macaulay inverse system. In this context, the
word "give" means, "give in a polynomial manner". The first paper in the series
proves, essentially, an existence theorem. The second and third papers in the
series construct the explicit formulas for the resolution. The present paper is
concerned with Artinian Gorenstein algebras of embedding codimension three. In
the third paper, "The structure of Gorenstein-linear resolutions of Artinian
algebras", the embedding codimension is arbitrary.
