The curse to third and fourth generations is tied specifically to the iniquity of utterly hating God as shown in the worship of other gods. I would think that this would be someone having already known of God and His mercy systematically choosing not retain God in their thoughts rebelliously worshiping the creature rather than the creator. We are not told what the curse will be here but, scripture suggests that the fathers are given over to that which is not convenient kjv@Romans:1 , their generations perhaps suffer after their consequences. Note that the threat of this was not enough to keep many from this; a testament to man's evil heart.
2012 - pBiblx2 Field Wise Bible System Version 2.0.9d - GPL3