I'm working on a project and I've used the Picard-Fuchs equation at a maximally unipotent monodromy point for a certain 1-dimensional family of Calabi-Yau 3-folds to calculate the A-model Yukawa coupling, and thus the generating function of the genus 0 GW invariants on the suspected mirror. I'm wondering if it's possible to have negative GW invariants even in genus 0. Also is it possible to have $n_d=0$ for all odd $d$, where the $n_d$ are defined to be the unique rational numbers fitting into the formula $N_l=\sum_{d|l} n_{l/d}d^{-3}$, where $N_d=I_{0,0,d}$ is the $d$-th genus 0, unpointed, GW invariant in degree d on a Calabi-Yau 3-fold with Picard rank 1. These numbers are also known as the instanton numbers.

To be more precise about my exact question: Suppose you have a CY 3-fold with Picard rank 1, so you can write any cohomology class in codim 2 as $dH$. Then we can write the GW invariants $$N_d=I_{0,0,dH}=\sum_{k|d} n_{d/k} k^{-3}.$$ Is it possible for these $n_{d/k}$'s to be negative for a few low degree terms, and zero for all odd degrees.