The paper 'Trisections, intersection forms and the Torelli group' by Peter Lambert-Cole quotes the following formula for the Casson invariant of a knot $K$ in a homology $3$-sphere in terms of the linking form $l$ on a Seifert surface $\Sigma$ for $K$ of genus $g$:
$$
\lambda'(K)=\sum\_{i=1}^g \big(l(a\_i,a\_i)l(b\_i,b\_i)-l(a\_i,b\_i)l(a\_i,b\_i)\big)+\sum\_{1 \le i<j \le g} \big(l(a\_i,a\_j)l(b\_i,b\_j)-l(a\_i,b\_j)l(a\_j,b\_i)\big).
$$
Here $\{a\_i,b\_i\}$ is a geometric symplectic basis for $\Sigma$.


Does anyone have a reference for this formula? I have looked for it in both Saveliev's and Akbulut & McCarthy's books, but I was not able to find anything similar.



Formula for the Casson invariant in terms of the linking form
Maybe you've already found a source or this is irrelevant by now, but I believe I took it from Morita's paper "Casson's invariant for homology 3-spheres and characteristic classes of surface bundles I". Specifically Proposition 3.2.


