A formula for the generalized Sato-Levine invariant

Let W be the generalized Sato-Levine invariant, that is, the unique Vassiliev invariant of order 3 for two-component links that is equal to zero on double torus links of type (1,k). It is proved that W-{beta}-(k{sup 3}-k)/6 where {beta} is the invariant of order 3 proposed by Viro and Polyak in the form of representations of Gauss diagrams and k is the linking number.